The calculation of valence shell ionization potentials by the ΔSCF method

Valence shell ionization potentials for several small molecules (HF, H₂O, CH₄, CO, H₂S, PH₃, SiH₄, SO₂ and F₂CO) are calculated by means of ab initio ΔSCF calculations on all the valence hole states of each molecule. The results are compared with the experimental low energy photoelectron spectra. In the case of the higher energy ion states, particular attention is paid to finding practical means for obtaining convergence of the ΔSCF iterations, and numerical evidence is presented, indicating that the ΔSCF procedure provides upper bounds to the energy of such states, at least for the cases studied herein. A new procedure, the ‘ combined ΔSCF ’ method, for the determination of a common set of molecular orbitals for use in the construction of wavefunctions for a number of ion states is described.     

How to determine vertical ionization potentials from photoelectron spectra

The center of gravity E_cg of a deconvoluted single direct photoionization band is a good estimate for the vertical ionization potential (VIP). This also holds for bands which are asymmetrically split by Jahn-Teller effect. Corresponding approximate formulae are given and applied to several experimental spectra, e.g. in order to reinterpret the second band of NH₃. Formulae for the difference between E_cg and VIP are derived. The most important effects in this respect are caused by anharmonicity of the ionic potential curve, by different force constants in the molecule and its ion, and by very high temperatures. A formula suitable for the determination of E_cg is given.     

Density functional calculation of the ionization potentials of small metallic particles

A Density Functional Pseudopotential method is used to compute the ionization potential IP of Sodium, Aluminium and Lead microparticles as a function of particle size. The model particles are formed by a central atom surrounded by successive coordination shells of first neighbours, second neighbours, etc. Maxima in IP are obtained for particles with filled coordination shells. The magnitude of IP correlates with the magnitude of the electron density in the region where the electron is extracted.     

Application of multiquantum ionization to measuring the ionization potentials of atoms and molecules of substances in the gas phase

A technique for measuring the ionization potentials of atoms and molecules is suggested which is distinguished by its accuracy and simplicity. N. E. Zhukovskii Air Force Engineering Academy, 40, Leningradskii Ave., Moscow, 125167, Russia. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 6, pp. 842–844, November–December, 1997.     

Perturbed Coulomb potentials in the Klein-Gordon equation via the asymptotic iteration method

The asymptotic iteration method is used to construct the exact energy eigenvalues for a Lorentz vector or a Lorentz scalar, and an equally mixed Lorentz vector and Lorentz scalar Coulombic potentials. Highly accurate and rapidly converging ground-state energies for Lorentz vector Coulomb with a Lorentz vector or a Lorentz scalar linear potential, , respectively, are obtained.     

Application of asymptotic iteration method to a deformed well problem

The asymptotic iteration method(AIM) is used to obtain the quasi-exact solutions of the Schr o¨dinger equation with a deformed well potential. For arbitrary potential parameters, a numerical aspect of AIM is also applied to obtain highly accurate energy eigenvalues. Additionally, the perturbation expansion, based on the AIM approach, is utilized to obtain simple analytic expressions for the energy eigenvalues.     

Nonlinear asymptotic calculation of the Kelvin-Helmholtz instability

The problem of periodic capillary-gravitational wave motion on the uniformly charged interface between two ideal immiscible incompressible liquids is solved in the third order of smallness. The lower liquid is assumed to be ideally conducting, while the upper one is a dielectric executing translational motion parallel to the interface with a constant velocity. A nonlinear frequency correction in the resonance form is found. It is shown that the positions of internal nonlinear resonances depend on the sum of the field and Weber parameters, the density ratio of the liquids, and the wave number. When the upper liquid is denser than the lower one, resonances are absent.     

Theoretical prediction of the second to fourth actinide ionization potentials

Theoretical values for the experimentally mostly undetermined second to fourth ionization potentials of the actinide elements Ac to Lr are presented. One set of results is based on relativistic ab initio pseudopotential calculations at the complete active space self-consistent field and multi-reference averaged coupled-pair functional level of theory, corrected for spin-orbit effects, combined with extrapolations of the correlation contributions to the basis set limit. A second set of values also takes into account the errors of the applied pseudopotentials with respect to all-electron multi-configuration self-consistent field calculations applying the Dirac-Coulomb Hamiltonian. The quality of the predictions is estimated from related calculations on the lanthanide elements La to Lu, where the experimental values are available.     

Twin position sensitive ionization chamber,utilizing backgammon and time projection method

The anomalous dependence of average prompt fission neutron (PFN) multiplicity on the fission fragment total kinetic energy of ²⁵²Cf(sf) was investigated using digital signal processing (DSP). A twin Frisch-grid ionization chamber (TGIC) was used for fission fragment (FF) spectroscopy and PFN was registered with help of fast neutron detector (FND) on liquid scintillator base. The DSP apparatus was build up around the 8-channel fast synchronously sampling waveform digitizers (WFD). It was found that the main limitation of the experimental method, developed in ref. [1] for investigation of the PFN properties in neutron induced fission reaction ²³⁵U(n,f), ²³⁹Pu(n,f) etc is related to the FF energy loses of in the target backing. A modification of the method was suggested to overcome such a limitation.     

Application of asymptotic iteration method to the Khare-Mandal and its PT-symmetric QES partner potential

We study the application of the asymptotic iteration method to the Khare-Mandal potential and its PT-symmetric partner. The eigenvalues and eigenfunctions for both potentials are obtained analytically. We have shown that although the quasi-exactly solvable energy eigenvalues of the Khare-Mandal potential are found to be in complex conjugate pairs for certain values of potential parameters, its PT-symmetric partner exhibits real energy eigenvalues in all cases.      

Application of the pseudopotential method to the calculation of the phase transition temperature

Pseudopotential formalism was used to describe the phase transition from a two-phase to a one-phase state in alloys with limited solubility. The combined use of the pseudopotential and static concentration wave methods for calculating the temperature of the order-disorder phase transition was generalized to the case of lattices with a basis. Numerical calculations were carried out for the limiting solubility curves in the system Cd-Zn and the order-disorder transition temperatures for Mg₃Cd, MgCd, and MgCd₃ superstructures.     

XF3 (X=N,P,As)价层电离势的运动方程耦合团簇理论计算

采用运动方程单双取代耦合团簇理论(EOM-CCSD)对XF₃(X=N,P,As)的价层垂直离势(VIP)进行了系统计算,同时对称匹配团簇组态相互作用(SAC-CI)、外价层格林函数(OVGF)以及部分三阶近似(P3)方法也被应用到目前计算.与已有的实验结果比较表明:EOM-CCSD计算的价层垂直电离势整体上与SAC-CI结果相近,而优于OVGF和P3理论结果,在整个价层上,EOM-CCSD结果与实验值总体差距约0.2 eV, 在外价层这种差距相对较小,在内 关键词： XF₃(X=N;P;As)')" href="#">XF₃(X=N;P;As) 垂直电离势 运动方程耦合团簇理论     

Direct calculation of ionization energies

The advantages of the propagator formalism, as a direct method of calculating ionization energies, are stressed. The propagator equations are derived for closed-shell systems using an operator method instead of the usual diagrammatic derivations. The equations enable the development of an interpretation of the ionization energies in terms of conceptually simple quantities, such as pair correlation energies and associated relaxation effects, and retain the idea of orbital ionization. Infinite summations appearing in the self-energy terms are replaced by finite expressions involving functions satisfying uncoupled inhomogeneous differential equations. Certain high-order propagator equations are derived, and a connection with the Bethe-Goldstone formulation of pair correlation is made. Several computational procedures are advocated as forming the basis for balanced calculations of atomic and molecular ionization energies.     

Application of the projection operator method in equilibrium statistical physics

In the framework of the Liouville equation formalism the projecton operator method is used in equilibrium statistical physics.     

渐近保持PIC算法在等离子体粒子模拟中的应用

针对准中性Vlasov-Poisson系统中多尺度物理参数共存的问题开展研究,采用渐近保持格式推导出与Vlasov方程相耦合的Poisson方程。数值模拟了一维等离子体在真空中的膨胀,比较了渐近保持PIC算法与传统PIC算法模拟结果的异同。结果表明：两种算法在满足多尺度中小尺度量限制的前提下,其结果保持高度一致;且在克服小尺度量束缚时,渐近保持PIC算法依然可以正确地模拟等离子体的物理行为,大大节省了计算时间。     

A model calculation of the asymptotic reduced α-amplitude

In a schematic model, microscopic wave functions are improved in such a way that they yield the appropriate asymptotic α-amplitude.     

��������PIC�㷨�ڵ�����������ģ���е�Ӧ��

针对准中性Vlasov-Poisson系统中多尺度物理参数共存的问题开展研究,采用渐近保持格式推导出与Vlasov方程相耦合的Poisson方程。数值模拟了一维等离子体在真空中的膨胀,比较了渐近保持PIC算法与传统PIC算法模拟结果的异同。结果表明：两种算法在满足多尺度中小尺度量限制的前提下,其结果保持高度一致;且在克服小尺度量束缚时,渐近保持PIC算法依然可以正确地模拟等离子体的物理行为,大大节省了计算时间。