The reactivity of radical-molecular addition reaction was studied in terms of density-functional theory (DFT) and Hartree-Fock theory (HFT). It was found that the DFT method can give more accurate estimated result tha...The reactivity of radical-molecular addition reaction was studied in terms of density-functional theory (DFT) and Hartree-Fock theory (HFT). It was found that the DFT method can give more accurate estimated result than the HFT method. The reason might be that the energy of the highest occupied molecular orbital (HOMO) in DFT is not the ionization energy, but rather represents the change in the total energy with respect to the change in occupation number of electrons in the HOMO, consistent with the concept of the transition state. The energy of HOMO in HFT is the ionization energy, which may represent more properly the property of the products and reactants themselves.展开更多
In this work, the effects of the pairing correlation on the properties of neutron drops N=6-50 trapped in a harmonic oscillator potential with ω = 10 Me V are investigated by comparing the results given by the Skyrme...In this work, the effects of the pairing correlation on the properties of neutron drops N=6-50 trapped in a harmonic oscillator potential with ω = 10 Me V are investigated by comparing the results given by the Skyrme Hartree-Fock and Hartree-FockBogoliubov theories with the density-dependent delta interaction(DDDI) pairing force. The results showed that the pairing correlation slightly made the neutron drops more bound, and increased the central neutron density, the spin-orbit and pseudo spin-orbit splittings. Thus, the pairing correlation must be accounted for to improve the Skyrme functional compared with the ab initio calculations. Furthermore, although the single-particle energy gaps with or without pairing were similar, the shell closures varied due to pair scattering. Here, the shell closures in neutron drops using the Sk M* parameter set and DDDI pairing force were found at N=8, 16, and 32.展开更多
Calculation of total energies of the electronic ground states of atoms forms the basis for the frozen-core pseudopotentials used in atomistic calculations of much larger scale. Reference values for these energies prov...Calculation of total energies of the electronic ground states of atoms forms the basis for the frozen-core pseudopotentials used in atomistic calculations of much larger scale. Reference values for these energies provide a benchmark for the validation of new software to calculate such potentials. In addition, basic atomic-scale electronic properties such as the (first) ionization energy provide a simple check on the approximation used in the calculation method. We present a comparison of the total energies and ionization energies of atoms Z = 1 - 92 calculated in density functional theory with several levels of exchange-correlation functional and the Hartree-Fock method, comparing ionization energies to experiment. We also investigate the role of relativistic treatment on these energies.展开更多
In this article, we analyse three related preconditioned steepest descent algorithms, which are partially popular in Hartree-Fock and Kohn-Sham theory as well as invariant subspace computations, from the viewpoint of ...In this article, we analyse three related preconditioned steepest descent algorithms, which are partially popular in Hartree-Fock and Kohn-Sham theory as well as invariant subspace computations, from the viewpoint of minimization of the corresponding functionals, constrained by orthogonality conditions. We exploit the geometry of the admissible manifold, i.e., the invariance with respect to unitary transformations, to reformulate the problem on the Grassmann manifold as the admissible set. We then prove asymptotical linear convergence of the algorithms under the condition that the Hessian of the corresponding Lagrangian is elliptic on the tangent space of the Grassmann manifold at the minimizer.展开更多
The spin-dependent nature of the nuclear tensor force is studied in detail within the relativistic HartreeFock approach. The relativistic formalism for the tensor force is supplemented with an additional Lorentz-invar...The spin-dependent nature of the nuclear tensor force is studied in detail within the relativistic HartreeFock approach. The relativistic formalism for the tensor force is supplemented with an additional Lorentz-invariant tensor formalism in the a-scalar channel, so as to take into account almost fully the nature of the tensor force brought about by the Fock diagrams in realistic nuclei. Specifically, the tensor sum rules are tested for the spin and pseudospin partners with and without nodes, to further understand the nature of the tensor force within the relativistic model. It is shown that the interference between the two components of nucleon spinors causes distinct violations of the tensor sum rules in realistic nuclei, mainly due to the opposite signs on the κ quantities of the upper and lower components, as well as the nodal difference. However, the sum rules can be precisely reproduced if the same radial wave functions are taken for the spin/pseudo-spin partners in addition to neglecting the lower/upper components,revealing clearly the nature of the tensor force.展开更多
Hartree-Fock calculations are carried out to describe some properties of 16O and 40Ca nuclei using the two forms of fish-bone potential (I and II). A computer simulation search program has been introduced to solve thi...Hartree-Fock calculations are carried out to describe some properties of 16O and 40Ca nuclei using the two forms of fish-bone potential (I and II). A computer simulation search program has been introduced to solve this problem. The Hilbert space was restricted to three dimensional variational space spanned by single spherical harmonic oscillator orbits. Binding energies, root mean square radii and form factors are found to have a good fit with experimental data.展开更多
Using Skyrme’s density dependent interaction the evolution of nuclear shells has been studied in Hartree-Fock formalism. Optimization of the strength of tensor interaction has been done in reproducing the observed sp...Using Skyrme’s density dependent interaction the evolution of nuclear shells has been studied in Hartree-Fock formalism. Optimization of the strength of tensor interaction has been done in reproducing the observed splitting of shell model states of 40,48Ca, 56Ni and 208Pb. Spin-orbit splitting in Ca-isotopes, 56Ni, 90Zr, N = 82 isotones, Sn-isotopes and evolution of gaps in Z, N=8, 20 have been reanalyzed with the inclusion of tensor interaction. For doubly shell closed nuclei it has been observed that tensor interaction is sensitive to spin saturation of nuclear shells.展开更多
The restoration of pseudo-spin symmetry（PSS） along the N = 32 and N = 34 isotonic chains and the physics behind are studied by applying the relativistic Hartree-Fock theory with the effective Lagrangian PKA1. Taking...The restoration of pseudo-spin symmetry（PSS） along the N = 32 and N = 34 isotonic chains and the physics behind are studied by applying the relativistic Hartree-Fock theory with the effective Lagrangian PKA1. Taking the proton pseudo-spin partners(π2s1/2, π1d3/2) as candidates, the systematic restoration of PSS along both isotonic chains is found from sulphur（S） to nickel（Ni）, while an obvious PSS violation from silicon（Si） to sulphur is discovered near the drip lines. The effects of the tensor force components are investigated, introduced naturally by the Fock terms, which can only partially interpret the systematics from calcium to nickel, whereas they fail for the overall trends. Further analysis following the Schr?dinger-like equation of the lower component of Dirac spinor shows that contributions from the Hartree terms dominate the overall systematics of the PSS restoration. Such effects can be self-consistently interpreted by the evolution of the proton central density profiles along both isotonic chains. In particular, the PSS violation is found to tightly relate to the dramatic changes from the bubble-like density profiles in silicon to the central-bumped ones in sulphur.展开更多
The equation of state of neutron stars is studied in the newly developed density dependent relativistic Hartree-Fock (DDRHF) theory with the effective interaction PKO1 and applied to describe the properties of neutron...The equation of state of neutron stars is studied in the newly developed density dependent relativistic Hartree-Fock (DDRHF) theory with the effective interaction PKO1 and applied to describe the properties of neutron stars. The results are compared with the recent observational data of compact stars and those calculated with the relativistic mean field (RMF) effective interactions. The maximum mass of neutron stars calculated with PKO1 is about 2.45 M ⊙, which consists with high pulsar mass from PSR B1516+02B recently reported. The influence of Fock terms on the cooling of neutron stars is discussed as well.展开更多
The quasiparticle resonances are investigated by examining three kinds of quasiparticle spectra, i.e., the density of quasiparticle states, the occupation number density, and the pair number density in the continuum S...The quasiparticle resonances are investigated by examining three kinds of quasiparticle spectra, i.e., the density of quasiparticle states, the occupation number density, and the pair number density in the continuum Skyrme Hartree-Fock-Bogoliubov theory with the Green’s function method. Taking the weakly bound nucleus 66Ca as an example, the quasiparticle resonant energies and widths extracted from these three kinds of quasiparticle spectra are compared. For the narrow resonances, the extracted resonant energy and the width are consistent with each other. However, it is difficult to use the density of quasiparticle states to identify the broad resonances due to the background of nonresonant continuum. By switching off the pairing potential and/or the Hartree-Fock(HF) potential respectively in the calculation of these quasiparticle spectra, the roles of HF mean-field and pairing correlations in the quasiparticle resonances are demonstrated clearly. It turns out that all the quasiparticle resonances corresponding to the deeply bound, weakly bound and positive-energy single-particle resonant states, are mainly contributed by the HF potential. The pairing potential helps to slightly increase the resonant energy and the width. However, the pairing potential is important to make the nucleons occupy the low-lying nonresonant continuum states near the threshold and take part in the pairing correlations here,especially for the partial waves with small angular momentum ?.展开更多
基于Gogny核子-核子有效相互作用,发展了适用于描写原子核裂变过程、不包含任何对称性限制以及三维时间相关的Hartree-Fock-Bogoliubov理论计算程序(Gogny-TDHFB Code for Fission).程序包含静态裂变势能面计算的多维度集体自由度约束HF...基于Gogny核子-核子有效相互作用,发展了适用于描写原子核裂变过程、不包含任何对称性限制以及三维时间相关的Hartree-Fock-Bogoliubov理论计算程序(Gogny-TDHFB Code for Fission).程序包含静态裂变势能面计算的多维度集体自由度约束HFB和裂变动力学计算的TDHFB两部分.在(x,y)方向采用形变谐振子基.在z方向上,为了描述裂变直至断点和断后的极端形变,采用Lagrange mesh方法.利用本程序,对240Pu的裂变势能路径和断点动力学过程进行了计算.结果表明,240Pu存在对称和非对称两条裂变路径;三轴形变可以显著降低第一(内)裂变位垒;对能在断裂过程中起着重要作用.展开更多
基金the Foundation of State Key Laboratory of Coal Conversion.
文摘The reactivity of radical-molecular addition reaction was studied in terms of density-functional theory (DFT) and Hartree-Fock theory (HFT). It was found that the DFT method can give more accurate estimated result than the HFT method. The reason might be that the energy of the highest occupied molecular orbital (HOMO) in DFT is not the ionization energy, but rather represents the change in the total energy with respect to the change in occupation number of electrons in the HOMO, consistent with the concept of the transition state. The energy of HOMO in HFT is the ionization energy, which may represent more properly the property of the products and reactants themselves.
基金the National Natural Science Foundation of China(Grant Nos.11405116,and 11775119).
文摘In this work, the effects of the pairing correlation on the properties of neutron drops N=6-50 trapped in a harmonic oscillator potential with ω = 10 Me V are investigated by comparing the results given by the Skyrme Hartree-Fock and Hartree-FockBogoliubov theories with the density-dependent delta interaction(DDDI) pairing force. The results showed that the pairing correlation slightly made the neutron drops more bound, and increased the central neutron density, the spin-orbit and pseudo spin-orbit splittings. Thus, the pairing correlation must be accounted for to improve the Skyrme functional compared with the ab initio calculations. Furthermore, although the single-particle energy gaps with or without pairing were similar, the shell closures varied due to pair scattering. Here, the shell closures in neutron drops using the Sk M* parameter set and DDDI pairing force were found at N=8, 16, and 32.
文摘Calculation of total energies of the electronic ground states of atoms forms the basis for the frozen-core pseudopotentials used in atomistic calculations of much larger scale. Reference values for these energies provide a benchmark for the validation of new software to calculate such potentials. In addition, basic atomic-scale electronic properties such as the (first) ionization energy provide a simple check on the approximation used in the calculation method. We present a comparison of the total energies and ionization energies of atoms Z = 1 - 92 calculated in density functional theory with several levels of exchange-correlation functional and the Hartree-Fock method, comparing ionization energies to experiment. We also investigate the role of relativistic treatment on these energies.
基金supported by the DFG SPP 1445:"Modern and universal first-principles methods for many-electron systems in chemistry and physics" and the EU NEST project BigDFT.
文摘In this article, we analyse three related preconditioned steepest descent algorithms, which are partially popular in Hartree-Fock and Kohn-Sham theory as well as invariant subspace computations, from the viewpoint of minimization of the corresponding functionals, constrained by orthogonality conditions. We exploit the geometry of the admissible manifold, i.e., the invariance with respect to unitary transformations, to reformulate the problem on the Grassmann manifold as the admissible set. We then prove asymptotical linear convergence of the algorithms under the condition that the Hessian of the corresponding Lagrangian is elliptic on the tangent space of the Grassmann manifold at the minimizer.
基金Supported by National Natural Science Foundation of China(11375076,11675065)the Fundamental Research Funds for the Central Universities(lzujbky-2016-30)
文摘The spin-dependent nature of the nuclear tensor force is studied in detail within the relativistic HartreeFock approach. The relativistic formalism for the tensor force is supplemented with an additional Lorentz-invariant tensor formalism in the a-scalar channel, so as to take into account almost fully the nature of the tensor force brought about by the Fock diagrams in realistic nuclei. Specifically, the tensor sum rules are tested for the spin and pseudospin partners with and without nodes, to further understand the nature of the tensor force within the relativistic model. It is shown that the interference between the two components of nucleon spinors causes distinct violations of the tensor sum rules in realistic nuclei, mainly due to the opposite signs on the κ quantities of the upper and lower components, as well as the nodal difference. However, the sum rules can be precisely reproduced if the same radial wave functions are taken for the spin/pseudo-spin partners in addition to neglecting the lower/upper components,revealing clearly the nature of the tensor force.
文摘Hartree-Fock calculations are carried out to describe some properties of 16O and 40Ca nuclei using the two forms of fish-bone potential (I and II). A computer simulation search program has been introduced to solve this problem. The Hilbert space was restricted to three dimensional variational space spanned by single spherical harmonic oscillator orbits. Binding energies, root mean square radii and form factors are found to have a good fit with experimental data.
文摘Using Skyrme’s density dependent interaction the evolution of nuclear shells has been studied in Hartree-Fock formalism. Optimization of the strength of tensor interaction has been done in reproducing the observed splitting of shell model states of 40,48Ca, 56Ni and 208Pb. Spin-orbit splitting in Ca-isotopes, 56Ni, 90Zr, N = 82 isotones, Sn-isotopes and evolution of gaps in Z, N=8, 20 have been reanalyzed with the inclusion of tensor interaction. For doubly shell closed nuclei it has been observed that tensor interaction is sensitive to spin saturation of nuclear shells.
基金Supported by National Natural Science Foundation of China(11675065,11711540016)
文摘The restoration of pseudo-spin symmetry（PSS） along the N = 32 and N = 34 isotonic chains and the physics behind are studied by applying the relativistic Hartree-Fock theory with the effective Lagrangian PKA1. Taking the proton pseudo-spin partners(π2s1/2, π1d3/2) as candidates, the systematic restoration of PSS along both isotonic chains is found from sulphur（S） to nickel（Ni）, while an obvious PSS violation from silicon（Si） to sulphur is discovered near the drip lines. The effects of the tensor force components are investigated, introduced naturally by the Fock terms, which can only partially interpret the systematics from calcium to nickel, whereas they fail for the overall trends. Further analysis following the Schr?dinger-like equation of the lower component of Dirac spinor shows that contributions from the Hartree terms dominate the overall systematics of the PSS restoration. Such effects can be self-consistently interpreted by the evolution of the proton central density profiles along both isotonic chains. In particular, the PSS violation is found to tightly relate to the dramatic changes from the bubble-like density profiles in silicon to the central-bumped ones in sulphur.
基金Supported by National Natural Science Foundation of China (10435010, 10775004, 10221003)Major State Basic Research Development Program (2007CB815000)
文摘The equation of state of neutron stars is studied in the newly developed density dependent relativistic Hartree-Fock (DDRHF) theory with the effective interaction PKO1 and applied to describe the properties of neutron stars. The results are compared with the recent observational data of compact stars and those calculated with the relativistic mean field (RMF) effective interactions. The maximum mass of neutron stars calculated with PKO1 is about 2.45 M ⊙, which consists with high pulsar mass from PSR B1516+02B recently reported. The influence of Fock terms on the cooling of neutron stars is discussed as well.
基金supported by the National Key R&D Program of China(Grant No.2018YFA0404400)the National Natural Science Foundation of China(Grant Nos.11621131001,11405116,and 11875075)
文摘The quasiparticle resonances are investigated by examining three kinds of quasiparticle spectra, i.e., the density of quasiparticle states, the occupation number density, and the pair number density in the continuum Skyrme Hartree-Fock-Bogoliubov theory with the Green’s function method. Taking the weakly bound nucleus 66Ca as an example, the quasiparticle resonant energies and widths extracted from these three kinds of quasiparticle spectra are compared. For the narrow resonances, the extracted resonant energy and the width are consistent with each other. However, it is difficult to use the density of quasiparticle states to identify the broad resonances due to the background of nonresonant continuum. By switching off the pairing potential and/or the Hartree-Fock(HF) potential respectively in the calculation of these quasiparticle spectra, the roles of HF mean-field and pairing correlations in the quasiparticle resonances are demonstrated clearly. It turns out that all the quasiparticle resonances corresponding to the deeply bound, weakly bound and positive-energy single-particle resonant states, are mainly contributed by the HF potential. The pairing potential helps to slightly increase the resonant energy and the width. However, the pairing potential is important to make the nucleons occupy the low-lying nonresonant continuum states near the threshold and take part in the pairing correlations here,especially for the partial waves with small angular momentum ?.
文摘基于Gogny核子-核子有效相互作用,发展了适用于描写原子核裂变过程、不包含任何对称性限制以及三维时间相关的Hartree-Fock-Bogoliubov理论计算程序(Gogny-TDHFB Code for Fission).程序包含静态裂变势能面计算的多维度集体自由度约束HFB和裂变动力学计算的TDHFB两部分.在(x,y)方向采用形变谐振子基.在z方向上,为了描述裂变直至断点和断后的极端形变,采用Lagrange mesh方法.利用本程序,对240Pu的裂变势能路径和断点动力学过程进行了计算.结果表明,240Pu存在对称和非对称两条裂变路径;三轴形变可以显著降低第一(内)裂变位垒;对能在断裂过程中起着重要作用.
