Using the unsymmetrical one-range addition theorems introduced by one of the authors with the help of complete orthonormal sets of $／varPsi ^／alpha $-exponential type orbitals （$／alpha = 1,0, - 1, - 2,...）$, this...Using the unsymmetrical one-range addition theorems introduced by one of the authors with the help of complete orthonormal sets of $／varPsi ^／alpha $-exponential type orbitals （$／alpha = 1,0, - 1, - 2,...）$, this paper presents the sets of series expansion relations for multicentre nuclear attraction integrals over Slater-type orbitals arising in Hartree--Fock--Roothaan equations for molecules. The final results are expressed through multicentre charge density expansion coefficients and basic integrals. The convergence of the series is tested by calculating concrete cases for arbitrary values of parameters of orbitals.展开更多
Using formulae for one- and two-electron integrals of Coulomb interaction potential fk （r） = r^-k with non-integer indices k established by one of the authors with the help of complete orthonormal sets of ψ^α-expo...Using formulae for one- and two-electron integrals of Coulomb interaction potential fk （r） = r^-k with non-integer indices k established by one of the authors with the help of complete orthonormal sets of ψ^α-exponential-type orbitals （α = 1, 0,-1,-2,…）, we perform the calculations for isoelectronic series of the He atom containing nuclear charges from 2 to 10, where k = 1 - μ （-1 〈 μ 〈 0）. For this purpose we have used the double-zeta approximation, the configuration interaction and coupled-cluster methods employing the integer-n Slater-type orbitals as basis sets. It is demonstrated that the results of calculations obtained are better than the numerical Hartree-Fock values.展开更多
Higher electric multipole moments for the ground-state electronic configuration of some polyatomicmolecules, i.e. CH4, NH3, H2O, were calculated from SCF-HFR wavefunctions using Slater-type orbital basis sets.The calc...Higher electric multipole moments for the ground-state electronic configuration of some polyatomicmolecules, i.e. CH4, NH3, H2O, were calculated from SCF-HFR wavefunctions using Slater-type orbital basis sets.The calculated results for electric multipole moments of these molecules are in good agreement with the theoretical andexperimental ones.展开更多
Numerical atomic orbitals have been successfully used in molecular simulations as a basis set,which provides a nature,physical description of the electronic states and is suitable for ■(N)calculations based on the st...Numerical atomic orbitals have been successfully used in molecular simulations as a basis set,which provides a nature,physical description of the electronic states and is suitable for ■(N)calculations based on the strictly localized property.This paper presents a numerical analysis for some simplified atomic orbitals,with polynomial-type and confined Hydrogen-like radial basis functions respectively.We give some a priori error estimates to understand why numerical atomic orbitals are computationally efficient in electronic structure calculations.展开更多
A closed analytical relation is derived for the two-center nuclear attraction integrals over Slater type orbitals (STOs) in terms of binomial coefficients. This formula can be used in highly accurate calculations of t...A closed analytical relation is derived for the two-center nuclear attraction integrals over Slater type orbitals (STOs) in terms of binomial coefficients. This formula can be used in highly accurate calculations of the nuclear at-traction integrals. The relationships obtained are valid for arbitrary values of quantum numbers and screening con-stants of STOs and location of nuclei.展开更多
A formulation previously presented by the authors for coulomb integrals was generalized to other two-center integrals, except exchange integral. Within this frame, molecular integrals were expressed in terms of some n...A formulation previously presented by the authors for coulomb integrals was generalized to other two-center integrals, except exchange integral. Within this frame, molecular integrals were expressed in terms of some new functions closely related to the well-known incomplete gamma functions and these functions recursively evaluated. Special issues arising in the case of hybrid integrals were addressed, and the results were compared with the ones found in the literature.展开更多
Hartree-Fock-Roothaan (HFR) calculations for ground states of some atoms, i.e. He, Be, Ne, Ar, and Kr have been performed using minimal basis sets of Slater type orbitals (STOs) with integer and noninteger principal q...Hartree-Fock-Roothaan (HFR) calculations for ground states of some atoms, i.e. He, Be, Ne, Ar, and Kr have been performed using minimal basis sets of Slater type orbitals (STOs) with integer and noninteger principal quan-tum numbers (integer n-STOs and noninteger n-STOs). The obtained total energies for these atoms using minimal basis sets of integer n-STOs are in good agreement with those in the previous literature. On the other hand, for the case of minimal basis sets of noninteger n-STOs, although the calculated total energies of these atoms agree well with the results in literature, some striking results have been obtained for atoms Ar and Kr. Our computational re-sults for the energies of atoms Ar and Kr are slightly better than those in literature, by amount of 0.00222 and 0.000054 a.u., respectively. The improvement in the energies of atoms Ar and Kr may result from the efficient cal-culations of one-center two-electron integrals over noninteger n-STOs. For some atomic ions in their ground state, HFR calculations have been carried out using minimal basis sets of noninteger n-STOs. The obtained total energies for these atomic ions are substantially lower than those available in literature.展开更多
Ab initio calculations of the orbital and the ground state energies of some open- and closed-shell atoms over Slater type orbitals with quantum numbers integer and Slater type orbitals with quantum numbers noninteger ...Ab initio calculations of the orbital and the ground state energies of some open- and closed-shell atoms over Slater type orbitals with quantum numbers integer and Slater type orbitals with quantum numbers noninteger have been performed. In order to increase the efficiency of these calculations the atomic two-electron integrals were expressed in terms of incomplete beta function. Results were observed to be in good agreement with the literature.展开更多
文摘Using the unsymmetrical one-range addition theorems introduced by one of the authors with the help of complete orthonormal sets of $／varPsi ^／alpha $-exponential type orbitals （$／alpha = 1,0, - 1, - 2,...）$, this paper presents the sets of series expansion relations for multicentre nuclear attraction integrals over Slater-type orbitals arising in Hartree--Fock--Roothaan equations for molecules. The final results are expressed through multicentre charge density expansion coefficients and basic integrals. The convergence of the series is tested by calculating concrete cases for arbitrary values of parameters of orbitals.
文摘Using formulae for one- and two-electron integrals of Coulomb interaction potential fk （r） = r^-k with non-integer indices k established by one of the authors with the help of complete orthonormal sets of ψ^α-exponential-type orbitals （α = 1, 0,-1,-2,…）, we perform the calculations for isoelectronic series of the He atom containing nuclear charges from 2 to 10, where k = 1 - μ （-1 〈 μ 〈 0）. For this purpose we have used the double-zeta approximation, the configuration interaction and coupled-cluster methods employing the integer-n Slater-type orbitals as basis sets. It is demonstrated that the results of calculations obtained are better than the numerical Hartree-Fock values.
文摘Higher electric multipole moments for the ground-state electronic configuration of some polyatomicmolecules, i.e. CH4, NH3, H2O, were calculated from SCF-HFR wavefunctions using Slater-type orbital basis sets.The calculated results for electric multipole moments of these molecules are in good agreement with the theoretical andexperimental ones.
基金The research for this paper has been enabled by the Alexander von Humboldt Foundation,whose support for the long term visit of Huajie Chen at Technische Universit¨at Berlin is gratefully acknowledged.
文摘Numerical atomic orbitals have been successfully used in molecular simulations as a basis set,which provides a nature,physical description of the electronic states and is suitable for ■(N)calculations based on the strictly localized property.This paper presents a numerical analysis for some simplified atomic orbitals,with polynomial-type and confined Hydrogen-like radial basis functions respectively.We give some a priori error estimates to understand why numerical atomic orbitals are computationally efficient in electronic structure calculations.
文摘A closed analytical relation is derived for the two-center nuclear attraction integrals over Slater type orbitals (STOs) in terms of binomial coefficients. This formula can be used in highly accurate calculations of the nuclear at-traction integrals. The relationships obtained are valid for arbitrary values of quantum numbers and screening con-stants of STOs and location of nuclei.
文摘A formulation previously presented by the authors for coulomb integrals was generalized to other two-center integrals, except exchange integral. Within this frame, molecular integrals were expressed in terms of some new functions closely related to the well-known incomplete gamma functions and these functions recursively evaluated. Special issues arising in the case of hybrid integrals were addressed, and the results were compared with the ones found in the literature.
文摘Hartree-Fock-Roothaan (HFR) calculations for ground states of some atoms, i.e. He, Be, Ne, Ar, and Kr have been performed using minimal basis sets of Slater type orbitals (STOs) with integer and noninteger principal quan-tum numbers (integer n-STOs and noninteger n-STOs). The obtained total energies for these atoms using minimal basis sets of integer n-STOs are in good agreement with those in the previous literature. On the other hand, for the case of minimal basis sets of noninteger n-STOs, although the calculated total energies of these atoms agree well with the results in literature, some striking results have been obtained for atoms Ar and Kr. Our computational re-sults for the energies of atoms Ar and Kr are slightly better than those in literature, by amount of 0.00222 and 0.000054 a.u., respectively. The improvement in the energies of atoms Ar and Kr may result from the efficient cal-culations of one-center two-electron integrals over noninteger n-STOs. For some atomic ions in their ground state, HFR calculations have been carried out using minimal basis sets of noninteger n-STOs. The obtained total energies for these atomic ions are substantially lower than those available in literature.
文摘Ab initio calculations of the orbital and the ground state energies of some open- and closed-shell atoms over Slater type orbitals with quantum numbers integer and Slater type orbitals with quantum numbers noninteger have been performed. In order to increase the efficiency of these calculations the atomic two-electron integrals were expressed in terms of incomplete beta function. Results were observed to be in good agreement with the literature.
