Structures, stabilities and spectral properties of borospherene B44− and metalloborospherenes MB440/− (M = Li, Na, and K)

Abstract

Density functional theory (DFT) and time-dependent density functional theory (TD-DFT) calculations are carried out to study the stabilities, photoelectron, infrared, Raman and electronic absorption spectra of borospherene B44− and metalloborospherenes MB440/− (M = Li, Na, and K). It is found that all atoms can form stable exohedral metalloborospherenes M&B440/−, whereas only Na and K atoms can be stably encapsulated inside B440/− cage. In addition, relative energies of these metalloborospherenes suggest that Na and K atoms favor exohedral configuration. Importantly, doping of metal atom can modify the stabilities of B44 with different structures, which provides a possible route to produce stable boron clusters or metalloborospherenes. The calculated results suggest that B44 tends to get electrons from the doped metal. Metalloborospherenes MB44− are characterized as charge-transfer complexes (M2+B442−), where B44 tends to get two electrons from the extra electron and the doped metal, resulting in similar features with anionic B442−. In addition, doping of metal atom can change the spectral features, such as blueshift or redshift and weakening or strengthening of characteristic peaks, since the extra metal atom can modify the electronic structure. The calculated spectra are readily compared with future spectroscopy measurements and can be used as fingerprints to identify B44− and metalloborospherenes.

Detection of genuine n-qubit entanglement via the proportionality of two vectors

“…(18) becomes |πψ 1···n = |πψ ℓ1 R1 |πψ ℓ2 R2 · · · |πψ ℓm Rm . (20) Then, in light of Lemma 4, Eq. (19) holds.…”

“…To detect multi genuine entanglement, previous articles proposed linear and nonlinear entanglement witnesseses [5]- [15], Bell-like inequalities [16], and generalized concurrence [17][18][19]. In [20][21][22][23][24][25], sufficient conditions to detect and measure genuine bipartite and tripartite entanglement for pure states were presented. Very recently, a general criterion was proposed for detecting multilevel entanglement in multiparticle quantum states [26] and a necessary and sufficient criterion for the separability of bipartite mixed states [27].…”

Ultrahigh differential mobility and velocity of Néel domain walls in spin valves with planar-transverse polarizers and perpendicularly injected small currents

“…Nevertheless, rigorous profile and velocity of TDWs under an arbitrary UTMF are hard to obtain due to the mismatch between symmetries in different energy terms in transverse direction. Since we focus on the traveling-mode at low current density, the 1D-AEM [28][29][30][31][32] on LLG equation shall provide useful information. Recalling the results in Sec.…”

“…Note that L is the same 1D self-adjoint Schrödinger operator as given in Refs. [28][29][30][31][32]. Following the "Fredholm alternative", by demanding θ ′ 0 (kernel of L ) to be orthogonal to the function F s defined in Eq.…”

“…Also, we provide analytics for parallel and perpendicular polarizers which perfectly explains existing simulations. At last, further boosting of DWs by uniform transverse magnetic fields (UTMFs) are studied with the help of onedimensional asymptotic expansion method (1D-AEM) [28][29][30][31][32].…”