TOMBO: All-electron mixed-basis approach to condensed matter physics

2019

Phys. Rev. B

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In order to calculate x-ray emission spectroscopy (XES) spectra, we apply the GW + Bethe-Salpeter equation (GW + BSE) method on a basis of extended quasiparticle theory which enables one to treat an arbitrary excited state as an initial state, because the initial state in the XES process is a highly excited state with a core hole. Compared to the preexisting experimental data of XES fluorescence photon energy, the calculated GW + BSE results give values with about 1-eV accuracy, which is comparable to the previous results using the time dependent density functional theory with the SRC exchange-correlation functional, the equation of motion-coupled cluster single and double, and delta self-consistent field methods. Our GW + BSE results reproduce corresponding experimental XES spectra without missing any peak. The method can assign the excitonic configuration of each peak in XES spectra with the quasiparticle levels. As a result, the analysis of excitonic structure for each peak gives obvious interpretation concerning the relation between excitonic states and valence states.

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Ab initio simulations of x-ray emission spectroscopy with the GW+ Bethe-Salpeter equation method

Aoki

2019

Phys. Rev. B

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“…We use the standard one-shot GW approximation (G 0 W 0 ) by beginning with the LDA [32] for both the ground-state and excited-state configurations of isolated lithium, aluminum, and beryllium atoms and nitrogen, oxygen and lithium (diatomic) molecules with the bond lengths fixed at 1.106Å, 1.216Å, and 2.723Å, respectively, for N 2 , O 2 , and Li 2 (calculated with B3LYP/6-31G* [33]). We use the all-electron mixd basis, TOMBO code [34], in which both plane waves (PWs) and atomic orbitals (AOs) are used as basis functions. The face-centered cubic (fcc) unit cell with an edge length of 18Å is used for Li, Li 2 , and Al, and that of 12Å is used for Be, N 2 , and O 2 .…”

Section: Test Calculationsmentioning

confidence: 99%

A simple derivation of the exact quasiparticle theory and its extension to arbitrary initial excited eigenstates

The Journal of Chemical Physics

Ono

Isobe

2017

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The quasiparticle (QP) energies, which are minus of the energies required by removing or produced by adding one electron from/to the system, corresponding to the photoemission or inverse photoemission (PE/IPE) spectra, are determined together with the QP wave functions, which are not orthonormal and even not linearly independent but somewhat similar to the normal spin orbitals in the theory of the configuration interaction, by self-consistently solving the QP equation coupled with the equation for the self-energy. The electron density, kinetic and all interaction energies can be calculated using the QP wave functions. We prove in a simple way that the PE/IPE spectroscopy and therefore this QP theory can be applied to an arbitrary initial excited eigenstate. In this proof, we show that the energy-dependence of the self-energy is not an essential difficulty, and the QP picture holds exactly if there is no relaxation mechanism in the system. The validity of the present theory for some initial excited eigenstates is tested using the one-shot GW approximation for several atoms and molecules. * ohno@ynu.ac.jp

“…In our TOMBO code, AOs are constructed by a product of the numerical radial function in a logarithmic mesh and the analytic cubic harmonics. In particular for the valence AOs, the radial function is confined inside the non‐overlapping atomic sphere by subtracting a smooth quadratic function with the same amplitude and derivative at the atomic sphere . This quadratic function inside the sphere smoothly connects to the tail of the true AO outside the sphere.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we newly implemented the SOC in our all‐electron mixed basis code, TOMBO, although the mass‐velocity and Darwin terms, the so‐called semi‐relativistic terms, were already included . Here we show the explicit formula of the AO–AO, PW–AO, and PW–PW matrix elements of the SOC using the cubic harmonics.…”

Section: Introductionmentioning

confidence: 99%

Spin‐Orbit Coupling in All‐Electron Mixed Basis Approach

Nakashima

2019

Annalen der Physik

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In the evaluation of the spin-orbit coupling (SOC), the use of the L · S formula is invalid in the interatomic region where the effective potential is not spherically symmetric. This problem occurs in the LCAO, LMTO, and APW methods, while the plane-wave pseudopotential and PAW methods cannot treat the spin-orbit splitting (SOS) of core orbitals. To avoid these problems, the all-electron mixed basis approach is adopted, which uses both plane waves (PWs) and atomic orbitals (AOs) as a basis set. The general form S · V × p can be used for PWs, while the standard form L · S can be used for AOs, which are well localized inside the non-overlapping atomic sphere in the spherical potential region and composed of the numerical radial function on a logarithmic radial mesh and analytic cubic harmonics. The explicit formula of the AO-AO, PW-AO, and PW-PW matrix elements of the SOC for spin-polarized systems is presented. In particular, the AO-AO matrices are explicitly derived for p, d, and f orbitals. The method is applied to the SOS of core and valence levels in X-ray photoelectron spectra. The results are in excellent agreement with the available experimental data, which suggests the validity of the present method.