In this paper, derivation of analytical expressions for overlap integrals with the same and different screening parameters of Slater type orbitals (STOs) via the Fourier-transform method is presented. Consequently, it...In this paper, derivation of analytical expressions for overlap integrals with the same and different screening parameters of Slater type orbitals (STOs) via the Fourier-transform method is presented. Consequently, it is relatively easy to express the Fourier integral representations of the overlap integrals with same and different screening parameters mentioned as finite sums of Gegenbauer, Gaunt, binomial coefficients, and STOs.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
In this Letter, we propose a three-dimensional （3D） image reconstruction method with a controllable overlapping number of elemental images in computational integral imaging. The proposed method can control the overl...In this Letter, we propose a three-dimensional （3D） image reconstruction method with a controllable overlapping number of elemental images in computational integral imaging. The proposed method can control the overlap- ping number of pixels coming from the elemental images by using the subpixel distance based on ray optics between a 3D object and an image sensor. The use of a controllable overlapping number enables us to provide an improved 3D image visualization by controlling the inter-pixel interference within the reconstructed pixels. To find the optimal overlapping number, we simulate the pickup and reconstruction processes and utilize the numerical reconstruction results using a peak signal-to-noise ratio （PSNR） metric. To demonstrate the feasibility of our work in optical experiments, we carry out the preliminary experiments and present the results.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
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
文摘In this paper, derivation of analytical expressions for overlap integrals with the same and different screening parameters of Slater type orbitals (STOs) via the Fourier-transform method is presented. Consequently, it is relatively easy to express the Fourier integral representations of the overlap integrals with same and different screening parameters mentioned as finite sums of Gegenbauer, Gaunt, binomial coefficients, and STOs.
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.
基金supported in part by the IT R&D program of MKE/KEIT.[10041682,Development of high-definition 3D image processing technologies using advanced integral imaging with improved depth range]Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Science,ICT & Future Planning(No.2011-0030079)
文摘In this Letter, we propose a three-dimensional （3D） image reconstruction method with a controllable overlapping number of elemental images in computational integral imaging. The proposed method can control the overlap- ping number of pixels coming from the elemental images by using the subpixel distance based on ray optics between a 3D object and an image sensor. The use of a controllable overlapping number enables us to provide an improved 3D image visualization by controlling the inter-pixel interference within the reconstructed pixels. To find the optimal overlapping number, we simulate the pickup and reconstruction processes and utilize the numerical reconstruction results using a peak signal-to-noise ratio （PSNR） metric. To demonstrate the feasibility of our work in optical experiments, we carry out the preliminary experiments and present the results.
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.
