By use of complete orthonormal sets of ψα exponential-type orbitals (ψα-ETOs, α = 1, 0,-1,-2, ...) the series expansion formulas for the noninteger n* Slater-type orbitals (NISTOs) in terms of integer n Slater-ty...By use of complete orthonormal sets of ψα exponential-type orbitals (ψα-ETOs, α = 1, 0,-1,-2, ...) the series expansion formulas for the noninteger n* Slater-type orbitals (NISTOs) in terms of integer n Slater-type orbitals(ISTOs) are derived. These formulas enable us to express the overlap integrals with NISTOs through the overlap integrals over ISTOs with the same and different screening constants. By calculating concrete cases the convergence of the series for arbitrary values of noninteger principal quantum numbers and screening constants of NISTOs and internuclear distances is tested. The accuracy of the results is quite high for quantum numbers, screening constants and location of STOs.展开更多
A new analytical approach to the computation of the Fermi-Dirac （FD） functions is presented, which was suggested by previous experience with various algorithms. Using the binomial expansion theorem these functions a...A new analytical approach to the computation of the Fermi-Dirac （FD） functions is presented, which was suggested by previous experience with various algorithms. Using the binomial expansion theorem these functions are expressed through the binomial coefficients and familiar incomplete Gamma functions. This simplification and the use of the memory of the computer for the calculation of binomial coefficients may extend the limits to large arguments for users and result in speedier calculation, should such limits be required in practice. Some numerical results are presented for significant mapping examples and they are briefly discussed.展开更多
The formulae are established in position,momentum,and four-dimensional spaces for the one-range addition theorems of generalized integer and noninteger μ Coulomb,and exponential type correlated interaction potentials...The formulae are established in position,momentum,and four-dimensional spaces for the one-range addition theorems of generalized integer and noninteger μ Coulomb,and exponential type correlated interaction potentials with hyperbolic cosine（GCTCP and GETCP HC）.These formulae are expressed in terms of one-range addition theorems of complete orthonormal sets of Ψα-exponential type orbitals（Ψ α-ETO）,α-momentum space orbitals（α-MSO）,and zα-hyperspherical harmonics（zα-HSH） introduced.The one-range addition theorems obtained can be useful in the electronic structure calculations of atoms and molecules when the GCTCP and GETCP HC in position,momentum,and four-dimensional spaces are employed.展开更多
文摘By use of complete orthonormal sets of ψα exponential-type orbitals (ψα-ETOs, α = 1, 0,-1,-2, ...) the series expansion formulas for the noninteger n* Slater-type orbitals (NISTOs) in terms of integer n Slater-type orbitals(ISTOs) are derived. These formulas enable us to express the overlap integrals with NISTOs through the overlap integrals over ISTOs with the same and different screening constants. By calculating concrete cases the convergence of the series for arbitrary values of noninteger principal quantum numbers and screening constants of NISTOs and internuclear distances is tested. The accuracy of the results is quite high for quantum numbers, screening constants and location of STOs.
文摘A new analytical approach to the computation of the Fermi-Dirac （FD） functions is presented, which was suggested by previous experience with various algorithms. Using the binomial expansion theorem these functions are expressed through the binomial coefficients and familiar incomplete Gamma functions. This simplification and the use of the memory of the computer for the calculation of binomial coefficients may extend the limits to large arguments for users and result in speedier calculation, should such limits be required in practice. Some numerical results are presented for significant mapping examples and they are briefly discussed.
文摘The formulae are established in position,momentum,and four-dimensional spaces for the one-range addition theorems of generalized integer and noninteger μ Coulomb,and exponential type correlated interaction potentials with hyperbolic cosine（GCTCP and GETCP HC）.These formulae are expressed in terms of one-range addition theorems of complete orthonormal sets of Ψα-exponential type orbitals（Ψ α-ETO）,α-momentum space orbitals（α-MSO）,and zα-hyperspherical harmonics（zα-HSH） introduced.The one-range addition theorems obtained can be useful in the electronic structure calculations of atoms and molecules when the GCTCP and GETCP HC in position,momentum,and four-dimensional spaces are employed.
