Hyperbolic orbit and its variation of deep-space probe

While approaching the target body, the deep-space probe is orbiting hyperbolically before the maneuver. We discuss the variation of perturbed hyperbolic orbit using the method similar to that used in elliptic orbit. Ephemeris calculating and orbit control will benefit from the given analytical solution.     

同向电磁场中氢原子低能级简并的解除

利用同向电磁场的作用使氢原子低能级简并完全解除.     

Analytical Approach to Fractional Zakharov-Kuznetsov Equations by He＇s Homotopy Perturbation Method

The aim of this paper is to obtain the approximate analytical solution of a fractional Zakharov-Kuznetsov equation by using homotopy perturbation method （HPM）. The fractional derivatives are described in the Caputo sense. Several examples are given and the results are compared to exact solutions. The results reveal that the method is very effective and simple.     

Hydrogenic impurity in a quantum dot: Comparison between the variational and strong perturbation methods

A comparison is given between the variational and strong perturbation techniques. It has been shown that the variational method gives, in general, better results. Also, a new formulation is presented for the strong perturbation technique that depends on a simpler equivalent form of the perturbed part of the Hamiltonian. Moreover, common expressions which are valid for both treatments have been obtained. The results are applied to calculate the binding energy for a hydrogenic impurity placed in a finite confining potential spherical quantum dot in the states (1s), (2p) and (2s). The results obtained hitherto for a central impurity by using the strong perturbation technique are deduced in a much simpler way. As regards the off-central impurity some new expressions have been derived in both treatments. The numerical results for the two states (1s) and (2p) have also been investigated.     

Upper- and lower-bound Hylleraas–CI calculations for the nonrelativistic Po states of the 4He isotope

Extensive Hylleraas–CI calculations for the lowest P^o states of ⁴He were performed. The dependence of the variational energy values E_κ on the mass parameter κ given by κ=m/m is discussed. Furthermore, lower bounds to E_κ were calculated using variance minimization. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 25–30, 1998     

Direct calculation of ionization potentials of closed-shell atoms and molecules

Vertical ionization potentials, electron affinities and information about quasi-particles can be obtained by using the technique of the single-particle propagator. The expansion of the self-energy part up to third order perturbation theory can be evaluated numerically, but does not lead, in most cases, to satisfying results. A theoretical and numerical analysis of the diagrammatic expansion of the self-energy part requires the introduction of a renormalized interaction and renormalized hole and particle lines.     

SCF perturbation theory for unimolecular reactions

A CNDO/2 SCF perturbation theory is presented for interpreting the form of CNDO/2 potential energy surfaces of unimolecular reactions. The analysis is performed by calculating the energy change E arising from a distortion of the molecular geometry along the reaction coordinate. E is decomposed into different perturbational contributions which are appropriate for an interpretation of the perturbation energy E. Moreover, E is resolved into energy parts arising from a single occupied orbital and contributions due to pairwise orbital interactions. In this way one evaluates numerically how the form of the occupied and unoccupied orbitals determines the magnitude of E. If the distortion occurs along a definite symmetry coordinate, group-theoretical arguments can be applied to discuss the magnitude of characteristic components of the perturbation energy. The SCF perturbation theory is used to analyze the isomerization of ethylene, cis-2-butene and cis-2-butenenitrile.This work was partially supported by Nato-Grant No. 1072     

Relativistic perturbation theory of molecular structure

Summary The recently developed relativistic double perturbation theory is extended to handle relativistic changes of molecular structure more easily. This is achieved by simple coordinate scalings. Accurate higher order mixed perturbation energies for H ₂ ⁺ are calculated. The relativistic changes of bond energy,DE, of bond length,R _e , and especially of force constant,k, and of anharmonicity,a, are large, up to 100%·(Z/c)². The dominant contributions tok anda are due to the indirect change of the nonrelativistick anda connected with the relativistic change of bond length. Accordingly the relativistic changes obey Badger's and Gordy's rules (–RDEk).Dedicated to Prof. Klaus Ruedenberg in appreciation of his fundamental contributions to both formal theory and physical explanations in quantum chemistry     

The ene reaction: Comparison of results of Hartree-Fock,Møller-Plesset,CASSCF, and DFT calculations

Structural and energetic aspects of the ene reaction were investigated using a variety of computational methods incorporating different ways of accounting for electron correlation. Compared to the noncorrelated Hartree-Fock method, opposing trends were observed in the geometry of the transition state when using the Complete Active Space-Self Consistent Field (CASSCF) method versus Møller-Plesset and density functional theory (DFT) methods. For reproducing experimental results, both Møller-Plesset and DFT methods appear to be successful, while the CASSCF method failed to reproduce the experimental energy changes. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62: 509–514, 1997