Finite-difference-pseudopotential method: Electronic structure calculations without a basis

Non-degenerate two photon absorption spectra of Si nanocrystallites

“…RESULT Figure 1 shows the non-degenerate TPA coefficient β xx (ω 1 , ω 2 ) of hydrogenated cubic Si nanocrystallites of size l = 1 ∼ 4 (nm) as a function of ω 1 with a fixed excite light frequency, ω 2 = 2.4(eV). In the calculation, we used the Hamiltonian matrix discretized into N = L 3 (L = 32 ∼ 80) cubic meshes in real space, which consists of the semi-empirical local pseudopotential [3] the kinetic energy operator in the finite difference form [4] . The results were averaged over 2 − 16 random vectors depending on the system size.…”

“…In this paper, we develop a new algorithm for calculating TPA spectra by using semiempirical local pseudopotentials [3], finite difference method in real space [4], and a linearscaling time-dependent method which has been applied to the calculation of the linearresponse functions [5,6,7,8]. This efficient algorithm made it possible, for the first time, to calculate the size effect on the TPA spectra of very large nanocrystallites without using effective-mass approximation.…”

First-principles Calculation Method for Electronic Structures of Nanojunctions Suspended between Semi-infinite Electrodes

“…For example, the completeness of the basis set is always a concern, and treating nonperiodic systems with the plane wave basis leads to the waste of computational effort. A method which solves the Kohn-Sham equation directly on grid points in the real space has recently been introduced, [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] which avoids many of these problems. Within this method, boundary conditions are not constrained to be periodic, which permits the use of nonperiodic boundary conditions for clusters and a combination of periodic and nonperiodic boundary conditions for surfaces.…”

“…In this study, we have developed a first-principles procedure for electronic structure calculations of nanostructures suspended between crystalline electrodes, in which the real-space finite-difference method [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and the localizedorbital technique 21,22) are combined. Directly minimizing 23) the energy functional proposed by Mauri, Galli and Car (MGC), 24) we obtain satisfactorily the self-consistent solutions of the Kohn-Sham equation without usage of conventional self-consistent field techniques.…”

Path‐integral renormalization group treatments for many‐electron systems with long‐range repulsive interactions

“…In the PIRG method, the ground-state wave function is expressed by a linear combination of basis states, e.g., Slater determinants, in a truncated Hilbert space. While retaining the size of the truncated Hilbert space, the optimized basis states and the ground state are projected out numerically.To make the PIRG method applicable to more realistic systems, we extend the PIRG method with the real-space finite-difference (RSFD) approach in which every physical quantity is defined only on grid points in the discretized space [8][9][10][11] . In this endeavor, The process of "choosing more preferable basis states" becomes the main drawback with respect to the computational cost.…”