Masayuki Toyoda

Numerical evaluation of electron repulsion integrals for pseudoatomic orbitals and their derivatives

A numerical method to calculate the four-center electron-repulsion integrals for strictly localized pseudoatomic orbital basis sets has been developed. Compared to the conventional Gaussian expansion method, this method has an advantage in the ease of combination with O(N) density functional calculations. Additional mathematical derivations are also presented including the analytic derivatives of the integrals with respect to atomic positions and spatial damping of the Coulomb interaction due to the screening effect. In the numerical test for a simple molecule, the convergence up to 10(-5) hartree in energy is successfully obtained with a feasible cost of computation.

First-Principles Study on Electronic Structure and Spin State of Rutile (Ti,Co)O2 by Self-Interaction-Corrected Local Density Approximation: Role of Oxygen Vacancy

Electronic structure of rutile-TiO2 based dilute magnetic semiconductors (DMS) are investigated within self-interaction-corrected local density approximation (SIC-LDA). These results are compared with those calculated within standard LDA. We employ the Korringa–Kohn–Rostoker method combined with coherent potential approximation. It is found that high-spin state in (Ti,Co)O2 with O vacancy is predicted in the SIC-LDA. This result is in good agreement with the experimental results. As a result, we find that O vacancy in (Ti,Co)O2 is the origin of Co2+ high-spin state and SIC-LDA is indispensable to describe the correct electronic structure and spin state of TiO2-based DMS.

Fast spherical Bessel transform via fast Fourier transform and recurrence formula

We propose a new method for the numerical evaluation of the spherical Bessel transform. A formula is derived for the transform by using an integral representation of the spherical Bessel function and by changing the integration variable. The resultant algorithm consists of a set of the Fourier transforms and numerical integrations over a linearly spaced grid of variable k in Fourier space. Because the k-dependence appears in the upper limit of the integration range, the integrations can be performed effectively in a recurrence formula. Several types of atomic orbital functions are transformed with the proposed method to illustrate its accuracy and efficiency, demonstrating its applicability for transforms of general order with high accuracy.

Magnetodielectric detection of magnetic quadrupole order in Ba(TiO)Cu4(PO4)4 with Cu4O12 square cupolas

In vortex-like spin arrangements, multiple spins can combine into emergent multipole moments. Such multipole moments have broken space-inversion and time-reversal symmetries, and can therefore exhibit linear magnetoelectric (ME) activity. Three types of such multipole moments are known: toroidal; monopole; and quadrupole moments. So far, however, the ME activity of these multipole moments has only been established experimentally for the toroidal moment. Here we propose a magnetic square cupola cluster, in which four corner-sharing square-coordinated metal-ligand fragments form a noncoplanar buckled structure, as a promising structural unit that carries an ME-active multipole moment. We substantiate this idea by observing clear magnetodielectric signals associated with an antiferroic ME-active magnetic quadrupole order in the real material Ba(TiO)Cu4(PO4)4. The present result serves as a useful guide for exploring and designing new ME-active materials based on vortex-like spin arrangements.

Ferromagnetic Half Metallicity in Doped Chalcopyrite Semiconductors Cu(Al1−xAx)Se2 (A = 3d Transition-Metal Atoms)

We calculate electronic states and magnetic properties of 3d transition metal (TM) atom doped chalcopyrite-type materials Cu(Al1−xAx)Se2, where A = Ti, V, Cr, Mn, Fe, Co, and Ni, using the Korringa–Kohn–Rostoker Green’s function method. Some of the chalcopyrite compounds Cu(Al1−xAx)Se2 exhibit a stable ferromagnetic half metallic (FHM) state relative to a disordered local moment (DLM) state, which simulates a paramagnetic state. FHM states evince Curie temperatures (TC) above room temperature when low-concentration (10%) TM impurity ions Cr and Mn are doped at the host Al site, whereas Ti and V doping manifests half metallicity with TC nearly equal to and lower than room temperature, respectively. On the contrary, in Fe, Co, and Ni doped compounds instability of ferromagnetic states to DLM is obtained. The heats of formation by Mn doping in CuAlSe2 at the Al and Cu sites are estimated and the site preference at Al is realized.

Accurate finite element method for atomic calculations based on density functional theory and Hartree-Fock method

Abstract An accurate finite element method is developed for atomic calculations based on density functional theory (DFT) within local density approximation (LDA) and Hartree–Fock (HF) method. The radial wave functions are expanded by cubic Hermite spline functions on a uniform mesh for x = r , and all the associated integrals are analytically evaluated in conjunction with fitting procedures of the Hartree and the exchange–correlation potentials to the same cubic Hermite spline functions using a set of recurrence formulas. The total energy of atoms systematically converges from above, and the error algebraically decays as the mesh spacing decreases. When the mesh spacing d is taken to be 0.025 / Z bohr 1 / 2 , the total energy for an atom of atomic number Z can be calculated within error of 10 − 7 hartree for both the LDA and HF methods. The equal applicability of the method to DFT and the HF method with a similar degree of high accuracy enables the method to be a reliable platform for development of new functionals in DFT such as hybrid functionals.

Ab Initio Study on Pressure-Induced Phase Transition in LaCu3Fe4O12

The electronic structure and magnetic ordering in LaCu3Fe4O12 are theoretically studied by means of ab initio calculations. To clarify the microscopic mechanism for the experimentally observed phase transitions induced both by pressure and temperature, the cell-volume dependence of total energy is calculated. It is found that the electronic structure changes from insulating to metallic as the Cu valence shifts from nonmagnetic Cu3+ (S = 0) to spin-polarized Cu2+ (S = 1/2) at the transition pressure (or temperature). The electronic state of Cu is important since it is coupled with the metallicity of the electronic structure via the inter-site charge transfer. The pressure-induced phase transition in LaCu3Fe4O12 is explained by the difference in the bulk modulus between the insulating ground state and the metallic high-pressure phase. The mechanism for the temperature-induced phase transition is also proposed in terms of the magnetic configurational entropy of the magnetic moment of Cu spins.

Exchange functional by a range-separated exchange hole

An approximation to the exchange-hole density is proposed for the evaluation of the exact exchange energy in electronic structure calculations within the density-functional theory and the Kohn-Sham scheme. Based on the localized nature of density matrix, the exchange hole is divided into the short-range (SR) and long-range (LR) parts by using an adequate filter function, where the LR part is deduced by matching of moments with the exactly calculated SR counterpart, ensuring the correct asymptotic -1/r behavior of the exchange potential. With this division, the time-consuming integration is truncated at a certain interaction range, largely reducing the computation cost. The total energies, exchange energies, exchange potentials, and eigenvalues of the highest-occupied orbitals are calculated for the noble-gas atoms. The close agreement of the results with the exact values suggests the validity of the approximation.

LIBERI: Library for numerical evaluation of electron-repulsion integrals

Abstract We provide a C library, called LIBERI, for numerical evaluation of four-center electron repulsion integrals, based on successive reduction of integral dimension by using Fourier transforms. LIBERI enables us to compute the integrals for numerically defined basis functions within 10 − 5 Hartree accuracy as well as their derivatives with respect to the atomic nuclear positions. Damping of the Coulomb interaction can also be imposed to take account of screening effect. Program summary Program title: LIBERI Catalogue identifier: AEGG_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEGG_v1_0.html Program obtainable from: CPC Program Library, Queens University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 44 091 No. of bytes in distributed program, including test data, etc.: 1 692 085 Distribution format: tar.gz Programming language: C Computer: all Operating system: any Unix-like system RAM: 5–10 Mb Classification: 7.4 External routines: Lapack ( http://www.netlib.org/lapack/ ), Blas ( http://www.netlib.org/blas/ ), FFTW3 ( http://www.fftw.org/ ) Nature of problem: Numerical evaluation of four-center electron-repulsion integrals. Solution method: Four-center electron-repulsion integrals are computed for given basis function set, based on successive reduction of integral dimension using Fourier transform. Running time: 0.5 sec for the demo program supplied with the package.