Theoretical Studies on the Zintl Crystals Assembled by Al6ONa2 Clusters †

doi:10.7503/cjcu20190300

Abstract

Abstract:

The low energy isomers of Al₆ONa₂ were determined by genetic algorithm combined with ab initio calculations. The results reveal the strong magic behavior of O-centered Al-Na cluster with 26 electrons. The interaction of atomic O orbitals and Jellium orbitals of the metal moieties forms bonding orbitals localized on O atom and antibonding orbitals delocalized on the whole cluster. The hetero metal cluster with 26 electrons form closed s ²p ⁶S ²P ⁶D ¹⁰ shells and corresponds to a strong magic structure. The Na ⁺ cations are ionically bonded to the Al₆O ^2- anion. The electronic structures of Al₆O ^2- core also accord with the Wade-Mingos rule. Based on the peculiar stability of the superatomic anion Al₆O ^2-, we predicted two AB₂ clusters with Pn $3 ˉ$ m and Fd $3 ˉ$ m point groups by density functional theory(DFT) calculations. The binding energy of Al₆ONa₂ cluster is -23.44 eV, and the interaction energy between the clusters in the crystal structures is -1.19 and -1.53 eV. The electronic structures of the crystals indicate that both the assembled structures have semiconductor properties. The phonon dispersion curves and elastic constants show that the assembled crystals are dynamically and mechanically stability.

Key words: Magic cluster, Superatomic anion, Electronic structure, Cluster assemble

CLC Number:

O641

TrendMD:

ZHANG Zhaoyan,CHEN Hongshan. Theoretical Studies on the Zintl Crystals Assembled by Al₆ONa₂ Clusters ^†[J]. Chem. J. Chinese Universities, 2019, 40(11): 2354.

Figures/Tables 11

Fig.1 Low-energy isomers of Al6ONa2

Cluster	Symmetry	E_b/eV
Cluster	Symmetry	PAW-PBE	PBE/def2-TZVPP	MP2/def2-TZVPP
Al₆Na₂	$C 2 v$	-16.65	-16.27	-17.48
Al₆ONa₂-a	$C 2 v$	-23.44	-22.49	-23.30
Al₆ONa₂-b	$C 2 v$	-23.41	-22.46	-23.30
Al₆ONa₂-c	$D 3 d$	-23.33	-22.38	-23.32
Al₆ONa₂-d	$C 2 v$	-23.39	-22.44	-23.07

Cluster	Symmetry	E_b/eV
Cluster	Symmetry	PAW-PBE	PBE/def2-TZVPP	MP2/def2-TZVPP
Al₆Na₂	$C 2 v$	-16.65	-16.27	-17.48
Al₆ONa₂-a	$C 2 v$	-23.44	-22.49	-23.30
Al₆ONa₂-b	$C 2 v$	-23.41	-22.46	-23.30
Al₆ONa₂-c	$D 3 d$	-23.33	-22.38	-23.32
Al₆ONa₂-d	$C 2 v$	-23.39	-22.44	-23.07

Fig.2 Density of states(DOS) of Al6ONa2 cluster

Fig.3 Valance molecular orbitals of Al6ONa2

Species	PAW-PBE	PBE/def2-TZVPP	PAW-PBE(Pn $3 ˉ$ m)	PAW-PBE(Fd $3 ˉ$ m)
Q_Al/e	0.10/0.19/0.20	0.08/0.18/0.22	0.19	0.23
Q_Na/e	0.69	0.71	0.75	0.75
Q_O/e	-2.34	-2.39	-2.67	-2.87

Species	PAW-PBE	PBE/def2-TZVPP	PAW-PBE(Pn $3 ˉ$ m)	PAW-PBE(Fd $3 ˉ$ m)
Q_Al/e	0.10/0.19/0.20	0.08/0.18/0.22	0.19	0.23
Q_Na/e	0.69	0.71	0.75	0.75
Q_O/e	-2.34	-2.39	-2.67	-2.87

Fig.4 Unit cells of Al6ONa2 assembled crystals of Pn3ˉm(A) and Fd3ˉm(B)

Crystal	a/nm	R_Al—Al/nm	R_Al—O/nm	R_Al—Na/nm	R_C—C/nm	ρ/(g·cm^-3)	E_b/eV
Pn $3 ˉ$ m	0.91	0.29	0.20	0.32	0.79	0.98	-24.63
Fd $3 ˉ$ m	1.84	0.29	0.20	0.33	0.80	0.48	-24.97

Crystal	a/nm	R_Al—Al/nm	R_Al—O/nm	R_Al—Na/nm	R_C—C/nm	ρ/(g·cm^-3)	E_b/eV
Pn $3 ˉ$ m	0.91	0.29	0.20	0.32	0.79	0.98	-24.63
Fd $3 ˉ$ m	1.84	0.29	0.20	0.33	0.80	0.48	-24.97

Fig.5 Electronic band structures of the assembled crystals (A) Pn 3 ˉ m; (B) Fd 3 ˉ m.

Fig.6 Color-filled maps of ELF for the crystal structures in the (110) face of Pn3ˉm(A) and Fd3ˉm(B)

Fig.7 Phonon dispersion curves(A, B) and the density of states(A', B') for the Al6ONa2 assembled crystals (A, A') Pn 3 ˉ m; (B, B') Fd 3 ˉ m.

Crystal	C₁₁/GPa	C₁₂/GPa	C₄₄/GPa	B	G	E	ν	G/B
Pn $3 ˉ$ m	5.04	4.56	1.79	4.72	0.83	2.36	0.42	0.18
Fd $3 ˉ$ m	3.06	2.13	1.14	2.44	0.80	2.15	0.35	0.33

Crystal	C₁₁/GPa	C₁₂/GPa	C₄₄/GPa	B	G	E	ν	G/B
Pn $3 ˉ$ m	5.04	4.56	1.79	4.72	0.83	2.36	0.42	0.18
Fd $3 ˉ$ m	3.06	2.13	1.14	2.44	0.80	2.15	0.35	0.33

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Theoretical Studies on the Zintl Crystals Assembled by Al₆ONa₂ Clusters ^†

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