On Metal‐Atom Clusters IV. Photoionization thresholds and multiphoton ionization spectra of alkali‐metal molecules

Herrmann, André; Leutwyler, Samuel; Schumacher, Ernst; Wöste, L.

doi:10.1002/hlca.19780610141

Cited by 166 publications

(11 citation statements)

References 64 publications

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“…The resulting LGWΓ(EA) is in excellent agreement with the experimental value for these systems; the difference between LGWΓ(EA) and the experiment is about 0.1 eV. I: GW results for the ionization potential (IP) of neutral systems (GW(IP)), GW and LGWΓ results for the electron affinity (EA) of cationic systems (GW(EA) and LGWΓ(EA)), and the corresponding experimental data [30][31][32][33] Next, we show the GW + BSE (neutral) results and the GW (cation) results without BSE of the 1 st PAE corresponding to the HOMO-LUMO transition for Al, B, Li 3 , and Na 3 together with the experimental data [31,[34][35][36] (the peak corresponding to the A band observed by experiments for Na 3 [35] and Li 3 [36]) in Table II. The GW + BSE (neutral) results significantly underestimate the experimental PAEs as anticipated (the mechanism of the underestimation is reported in the previous research [16]), while the GW (cation) results without BSE are in fair agreement with the experimental PAEs; the difference between the GW method without BSE and the experiment is about 0.2 eV.…”

Section: B Comparison Of the Results For Ip/ea And 1 St Paementioning

confidence: 64%

“…Theoretically, the IP of the neutral systems must be identical to the EA of the cationic systems if the same atomic geometry is assumed for neutral and cationic systems. [29] Here, the one-shot GW results for the IP of the neutral systems (GW(IP)) are listed in Table I together with the oneshot GW and self-consistent LGWΓ results for the EA of the cationic systems (GW(EA) and LGWΓ(EA)), all of which should be compared with the experimental data, [30][31][32][33] for Al, B, Na 3 , and Li 3 . If we compare GW(EA) with GW(IP), the former is in better agreement with the experimental value for Al (the difference between GW(EA) and the experiment is 0.1 eV), while GW(EA) is in worse agreement with the experiment for Na 3 and Li 3 .…”

Section: B Comparison Of the Results For Ip/ea And 1 St Paementioning

confidence: 99%

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GW(Γ) method without the Bethe-Salpeter equation for photoabsorption energies of spin-polarized systems

2018

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The one-shot GW method beginning with the local density approximation (LDA) enables one to calculate photoemission and inverse photoemission spectra. In order to calculate photoabsorption spectra, one had to additionally solve the Bethe-Salpeter equation (BSE) for the two-particle (electron-hole) Green's function, which doubly induces the evaluation errors. It has been recently reported that the GW + BSE method significantly underestimates the experimental photoabsorption energies (PAEs) of small molecules. In order to avoid these problems, we propose to apply the GW(Γ) method not to the neutral ground state but to the cationic state to calculate PAEs without solving the BSE, which allows the rigorous one-to-one correspondence between the photoabsorption peak and the "extended" quasiparticle level. We applied the self-consistent LGWΓ method including the vertex correction to our method, and found that this method gives the PAEs of B, Na 3 , and Li 3 within the 0.1 eV accuracy.

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Section: B Comparison Of the Results For Ip/ea And 1 St Paementioning

confidence: 64%

Section: B Comparison Of the Results For Ip/ea And 1 St Paementioning

confidence: 99%

GW(Γ) method without the Bethe-Salpeter equation for photoabsorption energies of spin-polarized systems

2018

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“…Подробно исследована структура кластеров, состоящих из атомов щелочных металлов. Такие кластеры хорошо описываются моделью желе (jellium model) [58,59], что подтверждается циклом экспериментальных исследований [60][61][62][63][64][65][66][67]. Основная идея этой модели популярна в физике плазмы -положительные заряды равномерно размазываются по пространству, которое в данном случае находится внутри сферы конечного радиуса.…”

Section: большие кластерыunclassified

Systems of atoms with a short-range interaction

Smirnov¹

1992

Usp. Fiz. Nauk

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“…The resulting ionization potential (IP), electron affinity (EA), and optical gap E opt g (corresponding to the first dipole-allowed transition) of Na, Na 3 , B 2 , and C 2 H 2 calculated using the G 0 W 0 , GW, LGW, and LGWΓ W methods are listed in Tables I and II, together with the results of previous multireference single and double configuration interaction (MRDCI) calculations [28][29][30][31][32][33][34], configuration interaction single and double (CID) calculations [35], and the corresponding experimental values [11,12,[36][37][38][39][40][41][42][43][44][45]. For Na and Na 3 , the results of LGWΓ v are also listed in Table I.…”

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confidence: 99%

GWΓ+Bethe-Salpeter equation approach for photoabsorption spectra: Importance of self-consistentGWΓcalculations in small atomic systems

2016

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The self-consistent GWΓ method satisfies the Ward-Takahashi identity (i.e., the gauge invariance or the local charge continuity) for arbitrary energy (ω) and momentum (q) transfers. Its self-consistent firstprinciples treatment of the vertex Γ = Γ v or Γ W is possible to first order in the bare (v) or dynamicallyscreened (W) Coulomb interaction. It is developed within a linearized scheme and combined with the Bethe-Salpeter equation (BSE) to accurately calculate photoabsorption spectra (PAS) and photoemission (or inverse photoemission) spectra (PES) simultaneously. The method greatly improves the PAS of Na, Na 3 , B 2 , and C 2 H 2 calculated using the standard one-shot G 0 W 0 + BSE method that results in significantly redshifted PAS by 0.8-3.1 eV, although the PES are well reproduced already in G 0 W 0 . 1The quasiparticle (QP) equation method in many-body perturbation theory [1] is powerful for simultaneously determining the photoemission (or inverse photoemission) spectra (PES), i.e., QP energy spectra, and QP wave functions of target materials from first-principles. In this method, we expand the skeleton diagrams, i.e., the diagrams drawn with the full Green's function lines, for the self-energy in terms of the electron-electron Coulomb interaction v, and solve the QP equation, which is equivalent to the Dyson equation, as a self-consistent (SC) eigenvalue problem. The Hartree-Fock (HF) approach provides the first-order approximation. In Hedin's set of equations[1] known as the GWΓ approach, the exchange-correlation part of the self-energy is expressed aswhere G σ and Γ σ are the one-particle Green's function and the vertex function (σ is the spin index), respectively, and W = (1 − vP) −1 v represents the dynamically screened Coulomb interaction (P = −i σ G σ G σ Γ σ is the polarization function). The simplest approximation is to assume Γ σ = 1, which is called the GW approximation.It is well known that the SC GW method usually overestimates the energy gap [2, 3], while the one-shot GW approach (G 0 W 0 ) using the Kohn-Sham (KS) wave functions and eigenvalues[4] results in a better energy gap. However, quite recently, it has been pointed out that the photoabsorption spectra (PAS) for small molecules obtained by solving the Bethe-Salpeter equation (BSE) [5, 6] using G 0 W 0 are often significantly redshifted by about 1 eV [7,8]. The use of the Heyd-Scuseria-Ernzerhof (HSE) functional or the SC GW calculation (hereafter referred to as GW) improves the results, but they are not perfect [8,9]. For a spin-polarized sodium atom (Na) and trimer (Na 3 ), G 0 W 0 + BSE is extremely bad, although the G 0 W 0 QP energies are reasonably good [10]. The calculated and experimental [11] optical gaps for Na are 1.32 eV and 2.10 eV, respectively, and the calculated and experimental [12] PAS for Na 3 are shown in Fig. 1. These calculated results are far off from the experimental data [13].Here, we develop a GWΓ method, which involves a SC treatment of the vertex Γ = Γ v or Γ W and satisfies the Ward-Takahashi identity [14][...

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On Metal‐Atom Clusters IV. Photoionization thresholds and multiphoton ionization spectra of alkali‐metal molecules

Cited by 166 publications

References 64 publications

GW(Γ) method without the Bethe-Salpeter equation for photoabsorption energies of spin-polarized systems

GW(Γ) method without the Bethe-Salpeter equation for photoabsorption energies of spin-polarized systems

Systems of atoms with a short-range interaction

GWΓ+Bethe-Salpeter equation approach for photoabsorption spectra: Importance of self-consistentGWΓcalculations in small atomic systems

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