Construction of a nonlocal potential from the scattering amplitude in the born approximation

Within a framework of the Born approximation simplified by certain assumptions, a procedure is given which explicitly constructs a nonlocal potential that provides a fit to elastic scattering data. The data are assumed to consist of the scattering amplitude as a function of the momentum transfer over a finite range of energies. The constructed potential is unique only when the kernel of the nonlocal interaction is energy independent, or when its explicit energy dependence is known from information other than scattering data.     

Convergence problems in the solution of SCF equations

Some problems connected with the convergence of iterative solutions of the Hartree-Fock equations for the open shell systems are discussed. The nonuniqueness of the Hartree-Fock operator form is used. The method of iterating by the operator's power is developed for obtaining solutions of the Hartree-Fock equations. Some particular results for the molecules Li, Li are presented.     

Elastic scattering of electrons by H2 in the born approximation

This paper presents accurate computation of the differential cross sections for the elastic and vibrational excitation of ground state H₂ by fast electrons. The electronic matrix elements are evaluated at 20 internuclear separations and proper averaging over vibrational wavefunctions is carried out. The comparison to experiment yields excellent agreement. Different computational procedures appropriate for low and moderate values of momentum transfer are compared.     

An efficient and accurate approximation to double substitution coupled cluster wavefunctions

An approximate CCD theory in an efficient electron pair operator form has been applied to He₂ with very accurate results.     

A CSF-based multi-reference coupled pair approximation III. An application to F2, As2 and As+2

Using the newly developed multi-reference coupled pair approximation program code, the adiabatic potential curves of the ground states of F ₂, As ₂ and As ₂ ⁺ were calculated. Computed spectroscopic constants of these molecules were found to be in good agreement with experimental values. The resulting binding energy of As ₂ (3.86 eV) was compared with the experimental value of 3.99 eV [15] and the best multi-reference configuration interaction value (3.58 eV) reported previously by the present authors. The calculated first adiabatic ionization potential of As ₂ (9.67 eV) was found to be in good agreement with the experimental result. Received: 5 July 1997 / Accepted: 27 August 1997     

Hypervirial-perturbative approximation to the SCF eigenvalues of coupled oscillators

The hypervirial relations and perturbation theory are used in order to obtain analytical non-numerical expressions for the SCF eigenvalues of coupled oscillators.     

Time-averaging approximation in the interaction picture: absorption line shapes for coupled chromophores with application to liquid water

The time-averaging approximation (TAA), originally developed to calculate vibrational line shapes for coupled chromophores using mixed quantum/classical methods, is reformulated. In the original version of the theory, time averaging was performed for the full one-exciton Hamiltonian, while herein the time averaging is performed on the coupling (off-diagonal) Hamiltonian in the interaction picture. As a result, the influence of the dynamic fluctuations of the transition energies is more accurately described. We compare numerical results of the two versions of the TAA with numerically exact results for the vibrational absorption line shape of the OH stretching modes in neat water. It is shown that the TAA in the interaction picture yields theoretical line shapes that are in better agreement with exact results.     

Derivation from coupled channel equations of the resonance raman scattering amplitude for a diatomic molecule

The coupled equations of molecular collision theory can be formulated in such a way as to yield the amplitude for resonance Raman scattering of light by a diatomic molecule. Two variants of the method can be adopted, characterized by different choices for the potential matrices. All molecular potentials, either analytical or numerical, are treated on the same footing. Tests of accuracy are presented for the case of harmonic potentials intersected by linear potentials, for which an exact analytical solution can be given.     

A new technique for the early detection of stiffness in coupled differential equations and application to standard Runge-Kutta algorithms

Higher-order Runge-Kutta (RK) algorithms employing local truncation error (LTE) estimates have had very limited success in solving stiff differential equations. These LTEs do not recognize stiffness until the region of instability has been crossed after which no correction is possible. A new technique has been designed, using the local stiffness function (LSF), which can detect stiffness very early before instability occurs. The LSF is a normalized dimensionless ratio which is essentially based on the product of the step size and the geometric mean of all the slopes. It is exceedingly sensitive to the onset of stiffness. Together, the LSF and the LTE form a complementary pair which can cooperate to help solve some mildly stiff equations which were previously intractable to RK algorithms alone. Examples are given of implementation and LSF performance. Received: 18 September 1997 / Accepted: 13 February 1998 / Published online: 17 June 1998     

Corrections to the impulse approximation for use in electron compton scattering experiments

The breakdown of the impulse approximation for K-shell electrons in electron Compton scattering measurements on solids is parameterized in a form which makes it possible to assess the importance of this effect and where necessary to apply a suitable correction.     

A new method for solving the quantum hydrodynamic equations of motion: application to two-dimensional reactive scattering

The de Broglie-Bohm hydrodynamic equations of motion are solved using a meshless method based on a moving least squares approach and an arbitrary Lagrangian-Eulerian frame of reference. A regridding algorithm adds and deletes computational points as needed in order to maintain a uniform interparticle spacing, and unitary time evolution is obtained by propagating the wave packet using averaged fields. The numerical instabilities associated with the formation of nodes in the reflected portion of the wave packet are avoided by adding artificial viscosity to the equations of motion. The methodology is applied to a two-dimensional model collinear reaction with an activation barrier. Reaction probabilities are computed as a function of both time and energy, and are in excellent agreement with those based on the quantum trajectory method.     

An analytical approach to obtaining a valid solution to the secular equations for cis-disubstituted octahedral metal carbonyls

Using an analytical approach we have been able to obtain a valid solution to the secular equations for cis-ML₂(CO)₄ molecules. The solution has led to the relations by which carbonyl stretching force constants and interaction constants can be calculated directly from ¹²C¹⁶O stretching frequencies. It has been found that calculated force constants are in excellent agreement with those obtained from isotopic enrichment studies and exactly equal to those calculated through the iterative procedure employed by Jernigan et al.     

微流蒸发光散射检测器与毛细管液相色谱的联用及其在银杏叶提取物分析中的应用

将微流蒸发光散射检测器( μELSD)与毛细管液相色谱(cLC)联用,应用于中药银杏叶提取物及其分散片制剂的分离检测领域。首先对 μELSD仪器参数进行优化。通过调节漂移管温度与载气流量,提高了分析物的响应,并减小了噪声。然后,搭建了cLC-μELSD分离检测平台,其相对常规LC可大大减小实验试剂消耗。流动相A为0.05%(体积分数,下同)三氟乙酸(TFA)水溶液,流动相B为含0.05% TFA的甲醇溶液。最优的洗脱梯度条件为:0~10 min,5%B~25%B;10~25 min,25%B~38%B;25~35 min,38%B;35~40 min,38%B~42%B;40~55 min,42%B~50%B。银杏叶提取物和复杂中药制剂银杏叶提取物分散片都得到了较好的分离,并在其中鉴定到紫外波段几乎无吸收的重要内酯类活性成分白果内酯以及银杏内酯A、B和C。测定了不同厂家银杏叶提取物中萜类内酯洗脱时间的相对标准偏差,结果均不大于2.42%,表明该体系在目标物的分析上具有良好的重现性。实验证明所建立的cLC-ELSD体系在复杂中药体系的分离检测中有良好的应用性。     

The capture of inner-shell electrons in the strong-potential born (SPB) approximation

For the first time the capture of inner-shell electrons by protons is calculated by the SPB method without further approximation and using Hartree-Slater wavefunctions. The resulting cross-section has roughly the correct shape, but is much too large. The problem is traced to a loss of normalization caused by the SPB approximation. A suitably renormalized SPB gives close agreement with experiment.     

The parameterization and validation of generalized born models using the pairwise descreening approximation

Generalized Born Surface Area (GBSA) models for water using the Pairwise Descreening Approximation (PDA) have been parameterized by two different methods. The first method, similar to that used in previously reported parameterizations, optimizes all parameters against the experimental free energies of hydration of organic molecules. The second method optimizes the PDA parameters to compensate only for systematic errors of the PDA. The best models are compared to Poisson-Boltzmann calculations and applied to the computation of potentials of mean force (PMFs) for the association of various molecules. PMFs present a more rigorous test of the ability of a solvation model to correctly reproduce the screening of intermolecular interactions by the solvent, than its accuracy at predicting free energies of hydration of small molecules. Models derived with the first method are sometimes shown to fail to compute accurate potentials of mean force because of large errors in the computation of Born radii, while no such difficulties are observed with the second method. Furthermore, accurate computation of the Born radii appears to be more important than good agreement with experimental free energies of solvation. We discuss the source of errors in the potentials of mean force and suggest means to reduce them. Our findings suggest that Generalized Born models that use the Pairwise Descreening Approximation and that are derived solely by unconstrained optimization of parameters against free energies of hydration should be applied to the modeling of intermolecular interactions with caution.