Al6ONa2组装Zintl相晶体的理论研究

doi:10.7503/cjcu20190300

摘要/Abstract

摘要：

结合遗传算法和从头算方法确定了Al₆ONa₂的低能异构体. 揭示了以非金属为中心的Al-Na团簇的幻数行为. 金属团簇离域的凝胶轨道和非金属原子的价轨道作用形成定域在O原子上的成键轨道和离域在整个团簇上的反键轨道, 26个价电子形成s ²p ⁶S ²P ⁶D ¹⁰的闭合壳层强幻数电子结构. Al₆O ^2-与Na ⁺通过离子键结合, Al₆O ^2-的电子结构符合Wade-Mingos规则. 基于超原子阴离子Al₆O ^2-具有较强的热稳定性和化学惰性, 组装了具有Pn $3 ˉ$ m和Fd $3 ˉ$ m空间群的AB₂型晶体结构, Al₆ONa₂团簇的结合能为-23.44 eV, 组装结构中团簇单元间的相互作用能分别为-1.19和-1.53 eV. 晶体结构的电子结构分析表明, 2种组装晶体均为宽带隙半导体. 声子色散曲线和弹性常数的计算表明组装晶体具有良好的动力学稳定性.

关键词: 幻数团簇, 超原子阴离子, 电子结构, 团簇组装

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

中图分类号:

O641

TrendMD:

张兆燕,陈宏善. Al₆ONa₂组装Zintl相晶体的理论研究. 高等学校化学学报, 2019, 40(11): 2354.

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

图/表 11

Fig.1 Low-energy isomers of Al6ONa2

Table 1 Binding energy(Eb) of Al6Na2and Al6ONa2 clusters calculated using different models

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

Table 1 Binding energy(Eb) of Al6Na2and Al6ONa2 clusters calculated using different models

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

Table 2 AIM charge in Al6ONa2 cluster and assembled crystals

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

Table 2 AIM charge in Al6ONa2 cluster and assembled crystals

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)

Table 3 Cell parameter, interatomic distances, density and average binding energy Eb per cluster of the cluster assemble crystals

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

Table 3 Cell parameter, interatomic distances, density and average binding energy Eb per cluster of the cluster assemble crystals

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.

Table 4 Elastic constants(Cij), Bulk modulus(B), Shear modulus(G), Young’s modulus(E), and Poisson’s ratio(ν) of the crystal structures

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

Table 4 Elastic constants(Cij), Bulk modulus(B), Shear modulus(G), Young’s modulus(E), and Poisson’s ratio(ν) of the crystal structures

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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Al₆ONa₂组装Zintl相晶体的理论研究

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

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