Structure Prediction and Photoelectron Spectroscopy Study of Rare Earth-doped Silicon-based Clusters of MSiq7(M=Eu, Sm, Yb; q=0, -1)†

doi:10.7503/cjcu20180218

Abstract

Abstract:

The geometrical structures, relative stabilities, electronic properties and magnetism of anionic and neutral lanthanide metal-doped silicon clusters were systematically investigated by using the Saunders Kick global stochastic search technique combined with density functional theory(DFT) calculations at the PBEPBE/RE/SDD/Si/6-311+G(d) level of theory. The calculation results show that the ground state structure for anionic cluster is a 3D structure with the RE atom M sitting on top(or bottom) of the pentagonal bipyramid while adding another Si to the normal direction of it. The lowest energy structure of the neutral cluster is formed by substituting a Si atom on the equatorial surface of a distorted bicapped octahedral with an M atom. The SmS $i 7 -$ cluster has the highest binding energy and doping energy in the three rare earth doped clusters, indicating that SmS $i 7 -$ is the most stable cluster among them. When M atoms(M=Eu, Sm, Yb) were added into the Si₇ cluster, due to their unique atomic magnetism, the non-magnetic Si₇ cluster would be magnetized. In addition, the simulated photoelectron spectra(PES) of top-several isomers of each cluster were also presented, which could provide a theoretical basis for further experiments.

Key words: Atomic cluster, Density functional theory, Structural optimization, Magnetic property

CLC Number:

O641

TrendMD:

JIANG Xianming,WANG Huaiqian,CAO Yu,SUN Zhihui,CAO Yufang,WU Weibin. Structure Prediction and Photoelectron Spectroscopy Study of Rare Earth-doped Silicon-based Clusters of MS $i q 7$ (M=Eu, Sm, Yb; q=0, -1)^†[J]. Chem. J. Chinese Universities, 2018, 39(9): 1976.

Figures/Tables 7

Table 1 Symmetry type(Sym), spin multiplicity(SM), binding energy(Eb) per atom, doping energy(Ed) per atom and HOMO-LUMO energy gap(Egap) of the lowest-energy structures of both pure Sinq(n=7,8; q=0, -1) clusters and RE-doped MSiq7(M=Eu, Sm, Yb; q=0, -1) clusters

Cluster	Isomer	SM	Sym	E_b/eV	E_d/eV	E_gap/eV
Si₇	Ⅰ	1	D₅_h	3.56	—	2.16
S $i 7 -$	Ⅰ	2	D₅_h	3.65	—	0.59
Si₈	Ⅴ	1	C₂_v	3.45	—	1.11
S $i 8 -$	Ⅴ	2	T_d	3.64	—	0.46
EuSi₇	c	8	C₁	3.32	1.65	1.13
EuS $i 7 -$	a	9	C_s	3.51	2.51	0.25
SmSi₇	c	7	C₁	3.36	1.97	0.40
SmS $i 7 -$	a	6	C_s	3.56	2.94	0.30
YbSi₇	c	1	C₁	3.20	2.25	0.90
YbS $i 7 -$	a	2	C_s	3.47	2.20	0.36

Cluster	Isomer	SM	Sym	E_b/eV	E_d/eV	E_gap/eV
Si₇	Ⅰ	1	D₅_h	3.56	—	2.16
S $i 7 -$	Ⅰ	2	D₅_h	3.65	—	0.59
Si₈	Ⅴ	1	C₂_v	3.45	—	1.11
S $i 8 -$	Ⅴ	2	T_d	3.64	—	0.46
EuSi₇	c	8	C₁	3.32	1.65	1.13
EuS $i 7 -$	a	9	C_s	3.51	2.51	0.25
SmSi₇	c	7	C₁	3.36	1.97	0.40
SmS $i 7 -$	a	6	C_s	3.56	2.94	0.30
YbSi₇	c	1	C₁	3.20	2.25	0.90
YbS $i 7 -$	a	2	C_s	3.47	2.20	0.36

Table 2 Experimentally measured adiabatic and vertical detachment energies(ADEs and VDEs) from the photoelectron spectra compared to the calculated ground state or low-lying anion state ADEs and VDEs of RE-doped MSiq7(M=Eu, Sm, Yb; q=0, -1) clusters

Cluster	Isomer	Calculated		Experimental^[37]
Cluster	Isomer	ADE	VDE	ADE	VDE
$EuS i 7 -$	a	1.62	1.98	1.69±0.1	1.88
	b	1.62	2.01
	c	1.20	1.57
	d	1.41	1.96
SmS $i 7 -$	a	1.64	1.97	1.66±0.1	1.88
	b	1.60	1.95
	d	1.72	2.03
	c	1.21	1.69
YbS $i 7 -$	a	1.75	1.98	1.88±0.1	2.03
	c	1.45	1.95
	d	1.65	2.01
	b	1.80	2.07
	e	1.89	2.25
	f	2.03	2.26

Cluster	Isomer	Calculated		Experimental^[37]
Cluster	Isomer	ADE	VDE	ADE	VDE
$EuS i 7 -$	a	1.62	1.98	1.69±0.1	1.88
	b	1.62	2.01
	c	1.20	1.57
	d	1.41	1.96
SmS $i 7 -$	a	1.64	1.97	1.66±0.1	1.88
	b	1.60	1.95
	d	1.72	2.03
	c	1.21	1.69
YbS $i 7 -$	a	1.75	1.98	1.88±0.1	2.03
	c	1.45	1.95
	d	1.65	2.01
	b	1.80	2.07
	e	1.89	2.25
	f	2.03	2.26

Table 3 Relative energies for selected low-lying isomers of MSiq7(M=Eu, Sm, Yb; q=0, -1) with different density functional methods

Cluster	Isomer	Sym	ΔE/eV			Cluster	Isomer	Sym	ΔE/eV
Cluster	Isomer	Sym	PBEPBE	B3LYP	BPW91	Cluster	Isomer	Sym	PBEPBE	B3LYP	BPW91
EuSi₇	c	C₁	0	0	0	EuS $i 7 -$	a	C_s	0	0.14	0
	d	C_s	0.33	0.28	0.32		b	C_s	0.05	0	0.01
	a	C_s	0.36	0.42	0.37		c	C₁	0.06	0.02	0.03
	b	C_s	0.41	0.31	0.38		d	C_s	0.12	0.24	0.10
	g	C_s	0.65	0.94	0.64		e	C₂_v	0.30	0.41	0.29
	f	C₃_v	0.74	0.61	0.70		f	C₃_v	0.32	0.46	0.28
	e	C₂_v	0.78	0.87	0.78		g	C_s	0.44	0.59	0.42
	h	C_s	1.44	1.00	1.03		h	C_s	0.46	0.44	0.42
	k	C_s	1.45	1.34	1.39		i	C_s	1.07	1.19	1.05
Cluster	Isomer	Sym	ΔE/eV			Cluster	Isomer	Sym	ΔE/eV
Cluster	Isomer	Sym	PBEPBE	B3LYP	BPW91	Cluster	Isomer	Sym	PBEPBE	B3LYP	BPW91
	i	C_s	1.90	0.82	1.87		j	C_s	1.15	0.96	1.07
	j	C_s	1.93	1.69	1.86		k	C_s	1.24	1.20	1.16
	l	C_s	2.39	2.07	2.28		l	C_s	2.20	1.67	1.98
SmSi₇	c	C₁	0	0	0	SmS $i 7 -$	a	C_s	0	0.09	0
	a	C_s	0.28	0.30	0.23		b	C_s	0.10	0.81	0.01
	d	C_s	0.28	0.27	0.20		d	C_s	0.15	0.08	0.14
	b	C_s	0.34	0.23	0.15		c	C₁	0.27	0	0.25
	g	C_s	0.61	0.52	0.40		g	C_s	0.40	0.41	0.39
	f	C₃_v	0.64	0.49	0.66		f	C₃_v	0.49	0.27	0.40
	j	C_s	0.68	1.66	1.30		e	C₂_v	1.14	1.07	1.09
	e	C₂_v	0.77	0.89	0.85		k	C_s	1.31	1.53	1.61
	k	C_s	1.50	1.85	1.92		h	C_s	1.40	1.25	1.34
	i	C₃_v	1.71	1.77	1.83		j	C_s	1.75	1.88	1.67
	h	C_s	2.38	1.93	1.67		i	C₃_v	1.77	1.68	1.72
	l	C_s	2.61	2.55	2.34		l	C_s	1.81	1.34	1.78
YbSi₇	c	C₁	0	0	0	YbS $i 7 -$	a	C_s	0	0.13	0
	d	C_s	0.22	0.03	0.02		c	C_s	0.02	0.06	0
	a	C_s	0.29	0.09	0.10		d	C_s	0.04	0.14	0.03
	b	C_s	0.40	0.21	0.18		b	C_s	0.07	0	0.02
	g	C_s	0.66	0.46	0.45		e	C₂_v	0.29	0.39	0.27
	e	C₂_v	0.71	0.51	0.51		f	C₃_v	0.29	0.16	0.24
	f	C₃_v	0.85	0.66	0.61		i	C₂_v	0.31	0.50	0.30
	i	C₂_v	0.96	0.76	0.76		h	C_s	0.41	0.37	0.36
	h	C_s	0.99	0.79	0.76		g	C_s	0.43	0.56	0.41
	k	C_s	1.53	1.33	1.27		j	C_s	1.13	0.90	1.04
	j	C_s	1.90	1.70	1.64		k	C_s	1.25	1.19	1.18
	l	C_s	2.40	2.24	2.19		l	C_s	1.66	1.26	1.31

Table 3 Relative energies for selected low-lying isomers of MSiq7(M=Eu, Sm, Yb; q=0, -1) with different density functional methods

Cluster	Isomer	Sym	ΔE/eV			Cluster	Isomer	Sym	ΔE/eV
Cluster	Isomer	Sym	PBEPBE	B3LYP	BPW91	Cluster	Isomer	Sym	PBEPBE	B3LYP	BPW91
EuSi₇	c	C₁	0	0	0	EuS $i 7 -$	a	C_s	0	0.14	0
	d	C_s	0.33	0.28	0.32		b	C_s	0.05	0	0.01
	a	C_s	0.36	0.42	0.37		c	C₁	0.06	0.02	0.03
	b	C_s	0.41	0.31	0.38		d	C_s	0.12	0.24	0.10
	g	C_s	0.65	0.94	0.64		e	C₂_v	0.30	0.41	0.29
	f	C₃_v	0.74	0.61	0.70		f	C₃_v	0.32	0.46	0.28
	e	C₂_v	0.78	0.87	0.78		g	C_s	0.44	0.59	0.42
	h	C_s	1.44	1.00	1.03		h	C_s	0.46	0.44	0.42
	k	C_s	1.45	1.34	1.39		i	C_s	1.07	1.19	1.05
Cluster	Isomer	Sym	ΔE/eV			Cluster	Isomer	Sym	ΔE/eV
Cluster	Isomer	Sym	PBEPBE	B3LYP	BPW91	Cluster	Isomer	Sym	PBEPBE	B3LYP	BPW91
	i	C_s	1.90	0.82	1.87		j	C_s	1.15	0.96	1.07
	j	C_s	1.93	1.69	1.86		k	C_s	1.24	1.20	1.16
	l	C_s	2.39	2.07	2.28		l	C_s	2.20	1.67	1.98
SmSi₇	c	C₁	0	0	0	SmS $i 7 -$	a	C_s	0	0.09	0
	a	C_s	0.28	0.30	0.23		b	C_s	0.10	0.81	0.01
	d	C_s	0.28	0.27	0.20		d	C_s	0.15	0.08	0.14
	b	C_s	0.34	0.23	0.15		c	C₁	0.27	0	0.25
	g	C_s	0.61	0.52	0.40		g	C_s	0.40	0.41	0.39
	f	C₃_v	0.64	0.49	0.66		f	C₃_v	0.49	0.27	0.40
	j	C_s	0.68	1.66	1.30		e	C₂_v	1.14	1.07	1.09
	e	C₂_v	0.77	0.89	0.85		k	C_s	1.31	1.53	1.61
	k	C_s	1.50	1.85	1.92		h	C_s	1.40	1.25	1.34
	i	C₃_v	1.71	1.77	1.83		j	C_s	1.75	1.88	1.67
	h	C_s	2.38	1.93	1.67		i	C₃_v	1.77	1.68	1.72
	l	C_s	2.61	2.55	2.34		l	C_s	1.81	1.34	1.78
YbSi₇	c	C₁	0	0	0	YbS $i 7 -$	a	C_s	0	0.13	0
	d	C_s	0.22	0.03	0.02		c	C_s	0.02	0.06	0
	a	C_s	0.29	0.09	0.10		d	C_s	0.04	0.14	0.03
	b	C_s	0.40	0.21	0.18		b	C_s	0.07	0	0.02
	g	C_s	0.66	0.46	0.45		e	C₂_v	0.29	0.39	0.27
	e	C₂_v	0.71	0.51	0.51		f	C₃_v	0.29	0.16	0.24
	f	C₃_v	0.85	0.66	0.61		i	C₂_v	0.31	0.50	0.30
	i	C₂_v	0.96	0.76	0.76		h	C_s	0.41	0.37	0.36
	h	C_s	0.99	0.79	0.76		g	C_s	0.43	0.56	0.41
	k	C_s	1.53	1.33	1.27		j	C_s	1.13	0.90	1.04
	j	C_s	1.90	1.70	1.64		k	C_s	1.25	1.19	1.18
	l	C_s	2.40	2.24	2.19		l	C_s	1.66	1.26	1.31

Fig.1 Structures of the lower-lying isomers for pure Siq7/8(q=0, -1) clusters(Ⅰ—Ⅳ for Siq7; Ⅴ—Ⅹ for Siq8) and RE-doped MSiq7(M=Eu, Sm, Yb; q=0, -1) clusters(a—l) at the PBEPBE/RE/SDD/Si/6-311+G(d) level of theoryThe dark gray spheres stand for silicon atoms and the cyan ones for RE atoms.

Fig.2 Relative energies and simulated photoelectron spectra for the lowest-lying isomers of MSi7-[M=Eu(A1—A4), Sm(B1—B4), Yb(C1—C4)] clusters (A1), (B1), (C1) Isomer a; (A2), (B2), (C4) isomer b; (A3), (B4), (C2) isomer c; (A4), (B3), (C3) isomer d.

Table 4 Population of the natural charges and the electronic state of the lowest-energy RE-doped MSiq7(M=Eu, Sm, Yb; q=0, -1) clusters

Cluster	Isomer	State	RE	Si-1	Si-2	Si-3	Si-4	Si-5	Si-6	Si-7
EuSi₇	c	⁸A	0.96	-0.05	-0.24	-0.46	0.08	0.03	-0.26	-0.05
$EuS i 7 -$	a	⁹A	0.44	0.03	-0.37	-0.17	-0.30	-0.17	-0.30	-0.16
SmSi₇	c	⁷A	0.95	-0.05	-0.24	-0.45	0.08	0.03	-0.26	-0.06
SmS $i 7 -$	a	⁶A	0.38	0.03	-0.34	-0.19	-0.28	-0.20	-0.28	-0.12
YbSi₇	c	¹A	0.88	-0.04	-0.24	-0.46	0.11	0.04	-0.23	-0.06
YbS $i 7 -$	a	²A"	0.37	0.04	-0.28	-0.38	-0.17	-0.13	-0.17	-0.28

Table 4 Population of the natural charges and the electronic state of the lowest-energy RE-doped MSiq7(M=Eu, Sm, Yb; q=0, -1) clusters

Cluster	Isomer	State	RE	Si-1	Si-2	Si-3	Si-4	Si-5	Si-6	Si-7
EuSi₇	c	⁸A	0.96	-0.05	-0.24	-0.46	0.08	0.03	-0.26	-0.05
$EuS i 7 -$	a	⁹A	0.44	0.03	-0.37	-0.17	-0.30	-0.17	-0.30	-0.16
SmSi₇	c	⁷A	0.95	-0.05	-0.24	-0.45	0.08	0.03	-0.26	-0.06
SmS $i 7 -$	a	⁶A	0.38	0.03	-0.34	-0.19	-0.28	-0.20	-0.28	-0.12
YbSi₇	c	¹A	0.88	-0.04	-0.24	-0.46	0.11	0.04	-0.23	-0.06
YbS $i 7 -$	a	²A"	0.37	0.04	-0.28	-0.38	-0.17	-0.13	-0.17	-0.28

Table 5 Natural electron configuration, charge, magnetic moment of 6s, 4f, 5d, 6p and 6d states of M atom with M = Eu, Sm, Yb, along with total magnetic moment of the ground state structure of MSiq7(M=Eu, Sm, Yb; q=0, -1) clusters

Cluster	Valence electron configuration	RE Moment/μ_B							Molecule/μ_B
Cluster	Valence electron configuration	Charge/e	6s	4f	5d	6p	6d	Total	Molecule/μ_B
EuSi₇	6s^0.394f^6.975d^0.606p^0.096d^0.01	0.96	0.04	6.95	0.08	0.01	0.01	7.09	7
EuS $i 7 -$	6s^0.474f^6.925d^1.026p^0.196d^0.01	0.44	0.05	6.90	0.28	0.02	0	7.25	8
SmSi₇	6s^0.384f^5.965d^0.656p^0.096d^0.01	0.95	0.03	5.94	0.08	0	0.01	6.06	6
SmS $i 7 -$	6s^0.484f^5.785d^1.206p^0.196d^0.01	0.38	0.03	5.74	-0.02	0	0	5.75	5
YbSi₇	6s^0.554f^13.945d^0.486p^0.156d^0.01	0.88	0	0	0	0	0	0	0
YbS $i 7 -$	6s^0.604f^13.855d^0.886p^0.316d^0.02	0.37	0	0.08	0.12	0.01	0	0.21	1

Cluster	Valence electron configuration	RE Moment/μ_B							Molecule/μ_B
Cluster	Valence electron configuration	Charge/e	6s	4f	5d	6p	6d	Total	Molecule/μ_B
EuSi₇	6s^0.394f^6.975d^0.606p^0.096d^0.01	0.96	0.04	6.95	0.08	0.01	0.01	7.09	7
EuS $i 7 -$	6s^0.474f^6.925d^1.026p^0.196d^0.01	0.44	0.05	6.90	0.28	0.02	0	7.25	8
SmSi₇	6s^0.384f^5.965d^0.656p^0.096d^0.01	0.95	0.03	5.94	0.08	0	0.01	6.06	6
SmS $i 7 -$	6s^0.484f^5.785d^1.206p^0.196d^0.01	0.38	0.03	5.74	-0.02	0	0	5.75	5
YbSi₇	6s^0.554f^13.945d^0.486p^0.156d^0.01	0.88	0	0	0	0	0	0	0
YbS $i 7 -$	6s^0.604f^13.855d^0.886p^0.316d^0.02	0.37	0	0.08	0.12	0.01	0	0.21	1

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