HCO基态(X 2A′)与激发态(A 2A')的全维势能面与吸收光谱

本文利用神经网络方法构建了HCO体系的基态(X ²A'')与第一激发态(A ²A'')的高精度全维势能面. 利用含Davidson修正的内收缩MRCI-F12方法结合非常大的ACV5Z基组,共计算了4624个从头算点,且没有采取任何标度方案. 平衡构型、解离能、振动基频等与实验吻合很好. 与Ndengué等人的此前经标度得到的势能面相比,本文势能面计算的吸收光谱强度略大,峰值位置向更小的能量偏移了几十个波. 结果表明标度势能将会对动力学结果产生一些难以预测的影响. 然而,基于之前标度的势能面计算得到的共振能量比本文的结果更接近实验值,尽管如此,本文新发展的非标度高级别势能面仍有望为之后HCO体系的光解和碰撞动力学的实验和理论研究提供一些理论基础.     

Convergence acceleration of molecular dynamics methods for shocked materials using velocity scaling

ABSTRACT

In this work, a convergence acceleration method applicable to extended system molecular dynamics techniques for shock simulations of materials is presented. The method uses velocity scaling to reduce the instantaneous value of the Rankine–Hugoniot conservation of energy constraint used in extended system molecular dynamics methods to more rapidly drive the system towards a converged Hugoniot state. When used in conjunction with the constant stress Hugoniostat method, the velocity scaled trajectories show faster convergence to the final Hugoniot state with little difference observed in the converged Hugoniot energy, pressure, volume and temperature. A derivation of the scale factor is presented and the performance of the technique is demonstrated using the boron carbide armour ceramic as a test material. It is shown that simulation of boron carbide Hugoniot states, from 5 to 20 GPa, using both a classical Tersoff potential and an ab initio density functional, are more rapidly convergent when the velocity scaling algorithm is applied. The accelerated convergence afforded by the current algorithm enables more rapid determination of Hugoniot states thus reducing the computational demand of such studies when using expensive ab initio or classical potentials.     

Nonrelativistic scale anomaly, and composite operators with complex scaling dimensions

It is demonstrated that a nonrelativistic quantum scale anomaly manifests itself in the appearance of composite operators with complex scaling dimensions. In particular, we study nonrelativistic quantum mechanics with an inverse square potential and consider a composite s-wave operator O=ψψ. We analytically compute the scaling dimension of this operator and determine the propagator 〈0|TOO^†|0〉. The operator O represents an infinite tower of bound states with a geometric energy spectrum. Operators with higher angular momenta are briefly discussed.     

Elastic scattering, muon transfer, bound states and resonances in the three-body mesic molecular systems in the reduced adiabatic hyperspherical approach

The uniform method of numerical investigation of bound states and scattering processes 2→ 2 (including resonance states) in the Coulomb three-body (CTB) systems is developed. It is based on the adiabatic hyperspherical approach (AHSA) and includes the numerical realization and applications to the three-body mesic atomic systems. The results of calculations of bound states of these systems (including the local characteristics of the wave functions) and the scattering processes 2→ 2 (including the characteristics of the resonance states) are presented. This revised version was published online in August 2006 with corrections to the Cover Date.     

Resonances,metastable states and exponential decay laws in perturbation theory

Resonances which appear as perturbed bound states are discussed in the framework of Balslev-Combes theory. The corresponding metastable states are constructed using the formal perturbation expansion to orderN–1 for the (nonexistent) perturbed bound states. They are shown to have exponential decay in time governed by the complex resonance energies, up to a background of order 2N in the perturbation parameter. The results apply in lowest orderN=1 to the perturbation of bound states embedded in the continuum and in arbitrary order to cases like the Stark effect.Dedicated to Res Jost and Arthur Wightman     

Green’s function method in the problem of complex configurations in fermi systems with pairing

The Green’s function method is used to derive general equations for describing effects of pairing in Fermi systems where there are two types of interaction, two-particle and quasiparticle-phonon interaction. These equations generalize Bardeen-Cooper-Schrieffertheory to the case of complex configurations involving “strong” phonons. In the approximation of weak coupling to phonons, realistic equations that make it possible to describe excited states of nonmagic even-even nuclei with allowance for a single-particle continuum and complex configurations of the two quasiparticles ? phonon type are formulated for the first time. These equations are solved for an isovector E 1 resonance in the stable isotope ¹²⁰ Sn and in the unstable isotopes ^104,132Sn. It is shown that complex configurations must be taken into account in order to describe E1 excitations—in particular, in a broad energy region around the nucleon binding energy.

     

Scaling behaviour of the Hellmann potential with different strength parameters

We are reporting the scaling behaviour of the bound state energies associated with the Hellmann potential, with different strength parameters, using the Laguerre basis. We show the existence of a crossover phenomenon for the energy spectrum; the scaling laws for bound states as we approach the continuum are calculated. Close to the bound–resonance phase transition region, state energies and wavefunctions for the Hellmann potential, with different strength parameters, have been studied.     

Astrophysical <Emphasis Type="Italic">S</Emphasis>-factor for the radiative-capture reaction <Emphasis Type="Italic">p</Emphasis><Superscript>13</Superscript>C → <Superscript>14</Superscript>N<Emphasis Type="Italic">γ</Emphasis>

The possibility of describing experimental data on the astrophysical S factor for radiative proton capture on a ¹³C nucleus at energies in the range 0.03–0.8 MeV is considered within the potential cluster model involving forbidden states. It is shown that the energy dependence of this astrophysical S factor can be reasonably explained on the basis of the E1 transition to the ³ P ₁-wave bound state of the ¹⁴N nucleus in the p ¹³C channel from the ³ S ₁ wave of p ¹³C scattering in the resonance energy region around 0.55 MeV in the laboratory frame.     

The ground and low-lying excited potential curves of SO

A method is presented for approximating the effect of core electrons by a pseudopotential which is an extension of one previously presented by Dixon and Hugo. The pseudopotential is constructed in a fully ab initio manner from atomic SCF calculations. It is non-local in both radial and angular coordinates, but its matrix elements are none the less easy to evaluate. The method has been implemented within a multi-structure valence-bond framework. The approximations arising from the use of finite basis sets, both for the pseudopotential and for the valence wavefunction, inevitably lead to errors in calculated energies. However, these errors are largely atomic in origin. Thus, in addition to ab initio calculations we also use empirical atomsin-molecules corrections to minimize both basis set errors and atomic correlation errors. These method are applied to potential curves for 21 electronic states of the SO molecule. Comparison is made of the curves calculated using the ab initio multi-structure valence-bond method without and with the atoms-in-molecules corrections. The potential energy curves of three, previously unobserved, bound electronic states of SO are calculated. We estimate that these states, ¹Σ^-, ³Δ and ³Σ⁺, lie in the region of 3·2 to 3·4 eV above the ground state.     

A comparison of finite basis set and finite difference Hartree—Fock calculations for the open-shell (X 2Σ+) molecules BaF and YbF

A comparison is made of the accuracy with which the total electronic energy can be calculated by using the finite basis set approach (the algebraic approximation) and the finite difference method in calculations employing the Hartree—Fock model for the open shell ground (X ²Σ⁺) states of the fluorides BaF and YbF. The convergence of the calculations carried out within the algebraic approximation is monitored by employing systematically constructed basis sets of increasing size. The difference between the finite basis set and finite difference Hartree—Fock energies is 2.6μE _h for BaF and 2.8μE _h for YbF. Dipole moments determined within the algebraic approximation are also compared with the corresponding finite difference expectation values.     

Perturbative fragmentation of a vector color particle into bound states involving a heavy antiquark

Vector-particle fragmentation into possible S-wave bound states involving a heavy antiquark is considered for high-energy processes at high transverse momenta, and the relevant fragmentation function is calculated in the leading order of perturbative QCD for various patterns of the anomalous magnetic moment. One-loop equations describing the q ² evolution of the fragmentation-function moments that is caused by hard-gluon emission from the vector particle are derived. The integrated probabilities of fragmentation are obtained. The distribution of the bound state in the transverse momentum defined with respect to the fragmentation axis is calculated in the scaling limit.     

Ab initio calculations of lower resonant states of two-electron systems

The complex scaling and the stabilization methods are applied to calculating the parameters of the lowest resonance states of He and Li⁺. The results obtained by both methods are in a good agreement with the published data. It is shown that the wave functions constructed using the restricted configuration interaction approximation provide fairly accurate estimates of the resonance parameters. The possibility of using the stabilization method for calculating the phase shift function is also discussed.     

The complex scaling method for Dirac resonances

The method of complex scaling, usually used in atomic and molecular resonance calculations, is generalized to the Dirac equation. It is shown that Dirac resonances are associated with nonreal eigenvalues of the scaled Dirac Hamiltonian. The perturbation theory for the resonance parameters is also discussed.