A Direct Calculation of First-Order Wave Function of Helium

We develop a simple analytic calculation for the first order wave function of helium in a model in which nuclear charge screening is caused by repulsive coulomb interaction. The perturbation term, first-order correlation energy, and first-order wave function are divided into two components, one component associated with the repulsive coulomb interaction and the other proportional to magnetic shielding. The resulting first-order wave functions are applied to calculate second-order energies within the model. We find that the second-order energies are independent of the nuclear charge screening constant in the unperturbed Hamiltonian with a central coulomb potential.     

On the validity of the triple-dipole interaction as a representation of non-additive intermolecular forces

A complete partial wave analysis of the non-expanded non-additive coulomb interaction energy for three non-degenerate S-state atoms is given through third-order in the interatomic potential energy function. Pseudo state techniques are used to evaluate various partial wave components of the non-expanded second and third-order non-additive interaction energies for various isosceles triangular configurations of three interacting ground-state hydrogen atoms. These second and third-order non-expanded coulomb results are used, in conjunction with Heitler-London results for the first-order non-additive energies for the quartet spin state of the H(1s)-H(1s)-H(1s) interaction, to discuss the relative importance of various parts of the non-additive energy as a function of the geometrical configuration of the atoms, and the validity of both the non-expanded triple-dipole energy and the expanded Axilrod-Teller-Muto triple-dipole result as a representation of non-additive coulomb energies. For example, in the non-bonded interaction of three S-state atoms it appears that representing the non-additive energy by the non-additive coulomb energy is not reliable until the interatomic separations are somewhat larger than R*, the interatomic distance associated with the van der Waals minimum in the corresponding non-bonded dimer interaction. Further, the use of the triple-dipole interaction energy, with or without charge overlap corrections, to represent the non-additive coulomb energy is of doubtful validity until the interatomic separations are considerably greater than R*.     

Construction of minimizing sequence of multiparticle functions for calculating the spectrum of an atom

A method for calculating the states of a many-electron atom is proposed based on the representation of the wave function of the atom as a linear combination of multideterminant functions. Determinants are constructed from single-particle hydrogen-like functions in which the positive nuclear charge is replaced by a certain effective charge. For each single-particle function, the effective charge is calculated such that to take into account the interaction of a given electron with the spherically symmetric part of the screening charge distribution of remaining electrons. Examples of constructing approximating sequence of functions are given and results of calculations of energies of stationary states of the He and Li atoms are presented.     

准一维体系的电子关联的变分计算

对于具有库仑相互作用的准一维电子体系,本文提出了一种新的模型,得到了准一维体系的电子有效库仑势形式。在相关基函数理论框架下,根据电子气的集体振荡行为,给出该体系的多体波函数,并得到不同密度的电子体系的关联函数和关联能,本文得到的关联函数是恒正的,且满足归一化条件。     

Energy and fine structure of the lithium isoelectronic sequence

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类锂离子(Z=11～20)1s23p-1s2nd(n=6,7)的跃迁能和振子强度

用全实加关联(FCPC)方法计算类锂离予体系(Z=11～20)1s2nd(n=6,7)态的非相对论能量.相对论及质量极化效应对能量的修正用微扰论计算,量子电动力学(QED)修正利用有效核电荷方法估算.在此基础上计算了1s23p-1s2nd(n=6,7)的跃迁能及振子强度,对现有的关于1s2nd(n=6,7)态的精细结构的实验数据的可靠性提出质疑.     

Molecular g-tensors from analytical response theory and quasi-degenerate perturbation theory in the framework of complete active space self-consistent field method

The molecular g-tensor is an important spectroscopic parameter provided by electron para magnetic resonance (EPR) measurement and often needs to be interpreted using computational methods. Here, we present two new implementations based on the first-order and second-order perturbation theories to calculate the g-tensors within the complete-active space self-consistent field (CASSCF) wave function model. In the first-order method, the quasi-degenerate perturbation theory (QDPT) is employed for constructing relativistic CASSCF states perturbed with the spin–orbit coupling operator, which is described effectively in one-electron form with the flexible nuclear screening spin–orbit approximation introduced recently by us. The second-order method is a newly reported approach built upon the linear response theory which accounts for the perturbation with respect to external magnetic field. It is implemented with the coupled–perturbed CASSCF (CP-CASSCF) approach, which provides an equivalent of untruncated sum-over-states expansion. The comparison of the performances between the first-order and second-order methods is shown for various molecules containing light to heavy elements, highlighting their relative strength and weakness. The formulations of QDPT and CP-CASSCF approaches as well as the derivation of the second-order Douglas–Kroll–Hess picture change of Zeeman operators are given in detail.     

Scattering of Two Spinless Particles in 3D Formulation with Coulomb Admixtures

Scattering of two spinless charge particles for simple forces including coulomb admixtures is calculated without partial wave decomposition. The coulomb interaction being taken is of the type of screened coulomb potential. For the forces range is not infinite, the standard scattering theory is applied. The differential and total cross section are calculated and coulomb effects are shown.     

类锂体系(Z=21—30)基态1s22s电离能和相对论项能的理论计算

使用全实加关联方法和里兹(Ritz)变分方法计算了类锂体系(Z=21—30)基态1s²2s的非相对论能量和波函数；包括动能修正、电子-电子接触项、轨道-轨道相互作用项以及Darwin项的相对论修正和质量极化项由全实加关联波函数的一阶微扰给出，量子电动力学修正QED(quantum electronic dynamic)由有效核电荷方法和类氢公式计算；给出了中等核电荷的高电离类锂体系基态的电离能、相对论效应的项能(term energy)，并将计算结果与实验数据进行了比较，表明FCPC 关键词： 类锂体系 全实加关联 电离能 项能     

Phase Diagram of 2 × 2 Adsorbates at Surfaces with Hexagonal Symmetry

The phase diagram of a lattice-gas model for 2 2 2 adsorbates at surfaces with hexagonal symmetry has been investigated by Monte Carlo simulations. The model relies on repulsive interactions between the particles for distances up to second nearest neighbor sites. It is shown that first- or second-order phase transitions take place depending on the strength of the interactions. Strong first- or second-neighbor interactions are responsible for a first-order transition while for intermediate interaction strength a second-order transition is possible. The critical exponent for the susceptibility shows the expected value of the four-states Potts model in case of a second-order transition. The value of the critical exponent is reduced when the transition changes from first to second order.     

暗怪波的相互作用

以耦合非线性薛定谔方程为理论模型,数值研究了两个一阶暗怪波在正常色散单模光纤中的相互作用.基于一阶暗怪波精确解,采用分步傅里叶数值模拟法,从间距、相位差和振幅系数比方面讨论相邻两个一阶暗怪波之间的相互作用.基于二阶暗怪波精确解,讨论了两个一阶暗怪波的非线性相互作用.研究结果表明:同相位情况下,间距参数T1为0、5、20时,相邻两个一阶暗怪波相互作用激发产生“扭结型”暗怪波.相比较于单个暗怪波发生能量的弥散,“扭结型”暗怪波分裂形成多个次暗怪波.反相位情况下,间距参数T1为2、7、12时,相邻两个一阶暗怪波相互作用也可以激发产生“扭结型”暗怪波.并且“扭结型”暗怪波初始激发的空间位置偏离原始单个暗怪波的位置5.振幅系数比越大,该空间位置越接近5.二阶暗怪波可以看作是两个一阶暗怪波的非线性叠加,复合型和三组分型二阶暗怪波与相邻两个一阶暗怪波的相互作用略有相似.     

高离化类锂原子体系(Z=21～30)1s23p态的能级结构和振子强度

用全实加关联方法计算了类锂原子体系(Z=21～30)偶极跃迁1s22s -1s23p的跃迁能、振子强度以及1s23p态的精细结构劈裂.非相对论能量用Rayleigh -Ritz变分法确定;相对论修正和质量极化效应用微扰论计算;同时考虑了来自量子电动力学(QED)效应的修正.得到的理论结果与实验数据及物理规律符合的很好.     

On the performance of DFT/MRCI-R and MR-MP2 in spin–orbit coupling calculations on diatomics and polyatomic organic molecules

ABSTRACT

We have investigated the performance of different multi-reference quantum chemical methods with regard to electronic excitation energies and spin–orbit matrix elements (SOMES). Among these methods are two variants of the combined density functional theory and multi-reference configuration interaction method (DFT/MRCI and DFT/MRCI-R) and a multi-reference second-order Møller–Plesset perturbation theory (MR-MP2) approach. Two variants of MR-MP2 have been tested based on either Hartree–Fock orbitals or Kohn–Sham orbitals of the BH-LYP density functional. In connection with the MR-MP2 approaches, the first-order perturbed wave functions have been employed in the evaluation of spin–orbit coupling. To validate our results, we assembled experimental excitation energies and SOMES of eight diatomic and fifteen polyatomic molecules. For some of the smaller molecules, we carried out calculations at the complete active space self-consistent field (CASSCF) level to obtain SOMEs to compare with. Excitation energies of the experimentally unknown states were assessed with respect to second-order perturbation theory corrected (CASPT2) values where available. Overall, we find a very satisfactory agreement between the excitation energies and the SOMEs obtained with the four approaches. For a few states, outliers with regard to the excitation energies and/or SOMEs are observed. These outliers are carefully analysed and traced back to the wave function composition.     

The excitation energies and term energies of the excited states 1s2ns (n=3,4,5) and 1s2nf (n=4,5) of lithium-like systems of Z=11－20

In this paper, the full-core plus correlation (FCPC) and the Ritz method is extended to calculate the non-relativistic energies of 1s^2ns (n=3,4,5) and 1s^2nf (n=4,5) states and the wavefunctions of the lithium-like systems from Z=11－20. The mass-polarization and the relativistic correction including the kinetic-energy correction, the Darwin term, the electron－electron contact term, and the orbit－orbit interaction are evaluated perturbatively as the first-order correction. The contribution from quantum electrodynamic is also included by using the effective nuclear charge formula. The excited energies, the term-energy and fine structure, are given and compared with the other theoretical calculation and experimental results. It is shown that the correlative wave in the FCPC method embodies well the strong correlation between the 1s^2 core and the valence electron.     

Theoretical investigation of high-pressure phase transitions in Mg1-xSrxO

The stability of Mg_1-xSr_xO solid solution has been analyzed using charge transfer interaction potential (CTIP) model as well as density functional theory-based ab initio approach with Perdew–Burke–Ernzerhof (PBE) type parameterized generalized gradient approximation. The present CTIP model consists of long-range part as modified coulomb interactions and charge transfer forces whereas short-range part includes the van der Waals as well as Hafemeister Flygare type overlap repulsive interactions effective up to next nearest neighbor ions. The present study finds that under the influence of pressure host binary oxides as well as their solid solutions undergo B1→B2 structural phase transition in the pressure range of 54–495 GPa. The variation of ground state properties and transition pressures have also been analyzed as a function of Sr composition. The observed results for the end point members are in agreement to their experimental counterparts and the deviations have been discussed in terms of interactions taken into consideration in two approaches.     

二维均匀流与重力短峰波相互作用解析

短峰波和海流广泛分布于海洋之中,但二者的相互作用直到近些年才逐渐受到关注,根据速度势函数理论,推导二维均匀流与重力短峰波的相互作用,区别于之前的研究,推导时不考虑波面的毛细影响,避免了将位置变量(x)与时间变量(t)绑定的假设,使得二阶速度势函数包含了的时间(t)一阶项,从而给出了完整的二维流与短峰波交互作用的二阶解析解,对比结果说明上述考虑对于波流共同作用结果有影响,尤其是在波高较大时,影响更加明显,所得结果,可用于高波浪条件下海洋波浪与流相互作用的计算.     

Condensates of p-wave pairs are exact solutions for rotating two-component Bose gases

We derive exact analytical results for the wave functions and energies of harmonically trapped two-component Bose-Einstein condensates with weakly repulsive interactions under rotation. The isospin symmetric wave functions are universal and do not depend on the matrix elements of the two-body interaction. The comparison with the results from numerical diagonalization shows that the ground state and low-lying excitations consist of condensates of p-wave pairs for repulsive contact interactions, Coulomb interactions, and the repulsive interactions between aligned dipoles.     

Symmetry and surface energy coefficients with an effective interaction

Symmetry energy coefficients in the first and second order have been estimated by using an effective interaction developed in a previous paper. The rearrangement contribution to the first-order symmetry energy coefficient has also been estimated. The effect of neutron excess on the first- and second-order single particle energies of nuclear matter have been studied by determining the isotopic spin dependent part of the single particle potential. The 1s state single particle energies of²⁰⁸Pb and¹⁶O have been estimated from the single particle energy of nuclear matter by incorporating the values of the isotopic spin dependent part of the single particle potential. The surface energy coefficient has been determined by using the semi-infinite model in the Thomas Fermi approach.Financial assistance from University Grants Commission, New Delhi, is gratefully acknowledged. The authors are also grateful to Professor K. C. Pande and Dr. S. P. Pandya for helpful suggestions.     

Second-order picture of correlation effects in closed-shell atoms

Results of many calculations of the MP2 correlation energies for ground states of closed-shell atoms (referred to as MP2/CA energies) are presented and studied. Special attention is paid to laying down rules which govern the dependence on the nuclear charge (Z dependence) and on the number of electrons (N dependence) of (a) the partial wave (PW) increments to the second-order pair energies, (b) the second-order pair energies, and (c) the configurational pair energies. It has been found that these energy increments disclose many regularities useful from both the physical and computational points of view. Some of the MP2/CA increments are quasi-transferable between similar systems. The results obtained are used as a starting point for an extensive discussion of the methodological significance of MP2/CA studies, and for indicating various actual and potential areas of application of the MP2/CA approach in many-electron theory.