Theoretical and Quantitative Structural Relationships of the Electrochemical Properties of [M@C₈₂]@[SWCNT(5,5)-armchair-C_nH₂₀] (M = La, Y and n = 20–300) Nanostructure Complexes

Figures & data

FIGURE 1 The imaginary structures of 1–87. The form of M@C₈₂(a and b) was from Suzuki et al.^{[ 8 ]}

TABLE 1 The values of the relative structural coefficients of [SWCNT(5,5)-armchair-C_nH₂₀] (n = 20–190) – and [La@C₈₂]@[SWCNT(5,5)-armchair-C_nH₂₀]– and [Y@C₈₂]@[SWCNT(5,5)-armchair-C_nH₂₀]– ^a

			Adiabatic			[La@C82]@[SWCNT(5,5)-			[Y@C82]@[SWCNT(5,5)-
			electron			armchair-CnH20]30–47			armchair-CnH20]48–65
	Molecular	Point	affinity	^Red E
No.	formula	group	Eaa (eV)	(V)	No.	ΔG et(1)	ΔG et(2)	No.	ΔG et(1)	ΔG et(2)
1	C20H20	D 5d	0.34	−0.34	30	8.76	31.82	48	9.45	31.82
2	C30H20	D 5h	0.89	−0.89	31	21.45	44.51	49	22.14	44.51
3	C40H20	D 5d	0.67	−0.67	32	16.37	39.43	50	17.06	39.43
4	C50H20	D 5h	1.14	−1.14	33	27.21	50.27	51	27.90	50.27
5	C60H20	D 5d	1.56	−1.56	34	36.90	59.96	52	37.59	59.96
6	C70H20	D 5h	1.34	−1.34	35	31.82	54.88	53	32.51	54.88
7	C80H20	D 5d	1.61	−1.61	36	38.05	61.11	54	38.74	61.11
8	C90H20	D 5h	1.98	−1.98	37	46.58	69.64	55	47.27	69.64
9	C100H20	D 5d	1.71	−1.71	38	40.36	63.42	56	41.05	63.42
10	C110H20	D 5h	1.91	−1.91	39	44.97	68.03	57	45.66	68.03
11	C120H20	D 5d	2.24	−2.24	40	52.58	75.64	58	53.27	75.64
12	C130H20	D 5h	2.06	−2.06	41	48.43	71.49	59	49.12	71.49
13	C140H20	D 5d	2.13	−2.13	42	50.04	73.10	60	50.73	73.10
14	C150H20	D 5h	2.43	−2.43	43	56.96	80.02	61	57.65	80.02
15	C160H20	D 5d	2.35	−2.35	44	55.11	78.17	62	55.80	78.17
16	C170H20	D 5h	2.23	−2.23	45	52.35	75.41	63	53.04	75.41
17	C180H20	D 5d	2.53	−2.53	46	59.26	82.32	64	59.96	82.32
18	C190H20	D 5h	2.45	−2.45	47	57.42	80.48	65	58.11	80.48
Note. Values for [SWCNT(5,5)-armchair-CnH20] (n = 20–190) 1–18 were calculated and reported at the 6-31G* level (see Zhou^[ ^24 ^]). ^aThe compounds [M@C60]@[SWCNT(5,5)-armchair-CnH20]30–47 and 48–65 were not synthesized or reported. The data of ΔG et(n)(n = 1 and 2, kcal·mol^−1) for compounds 30–47 and 48–65 were calculated by the Rehm-Weller equation.

TABLE 2 The linear relationships between the values of the adiabatic electron affinity (E_aa in eV) and the values of the reduction potential ( ^Red E in V) of [SWCNT(5,5)-armchair-C_nH₂₀] (n = 20–190) – versus the first and second free energies of electron transfer (ΔG _et(n),n = 1,2 in kcal·mol⁻¹) of [La@C₈₂]@[SWCNT(5,5)-armchair-C_nH₂₀]– and [Y@C₈₂]@[SWCNT(5,5)-armchair-C_nH₂₀]–

			ΔG et(n)= aE +b
Equation
no.	E	n	a	b	R ^2
8	^Red E	1	−23.0610	0.9220	1.00
9	^Red E	1	−23.0620	1.6106	1.00
10	^Red E	2	−23.0610	23.9820	1.00
11	Eaa	1	23.0610	0.9220	1.00
12	Eaa	1	23.0620	1.6106	1.00
13	Eaa	2	23.0610	23.9820	1.00

TABLE 3 The values of the relative structural coefficients of [SWCNT(5,5)-armchair-C_nH₂₀] (n = 20–190) –, [La@C₈₂]@[SWCNT(5,5)-armchair-C_nH₂₀]–, and [Y@C₈₂]@[SWCNT(5,5)-armchair-C_nH₂₀]– ^a

						[La@C82]@[SWCNT(5,5)-armchair-CnH20]30–47					[Y@C82]@[SWCNT(5,5)-armchair-CnH20]48–65
						ΔG et(1)(kcal·mol^−1)		ΔG et(2)(kcal·mol^−1)			ΔG et(1)(kcal·mol^−1)		ΔG et(2)(kcal·mol^−1)
			Adiabatic electron
	Molecular	Point	affinity	^Red E		Eqs. 8	Rehm-	Eqs. 10	Rehm-		Eqs. 9	Rehm-	Eqs. 10	Rehm-
No.	formula	group	Eaa (eV)	(V)	No.	and 11	Weller	and 13	Weller	No.	and 12	Weller	and 13	Weller
19	C200H20	D 5d	2.49	−2.49	66	58.34	58.34	81.40	81.40	77	59.03	59.03	81.40	81.40
20	C210H20	D 5h	2.53	−2.53	67	59.26	59.26	82.32	82.32	78	59.96	59.96	82.32	82.32
21	C220H20	D 5d	2.57	−2.57	68	60.19	60.19	83.25	83.25	79	60.88	60.88	83.25	83.25
22	C230H20	D 5h	2.60	−2.60	69	60.88	60.88	83.94	83.94	80	61.57	61.57	83.94	83.94
23	C240H20	D 5d	2.64	−2.64	70	61.80	61.80	84.86	84.86	81	62.49	62.49	84.86	84.86
24	C250H20	D 5h	2.67	−2.67	71	62.49	62.49	85.55	85.55	82	63.18	63.18	85.55	85.55
25	C260H20	D 5d	2.71	−2.71	72	63.42	63.42	86.48	86.48	83	64.11	64.11	86.48	86.48
26	C270H20	D 5h	2.74	−2.74	73	64.11	64.11	87.17	87.17	84	64.80	64.80	87.17	87.17
27	C280H20	D 5d	2.77	−2.77	74	64.80	64.80	87.86	87.86	85	65.49	65.49	87.86	87.86
28	C290H20	D 5h	2.80	−2.80	75	65.49	65.49	88.55	88.55	86	66.18	66.18	88.55	88.55
29	C300H20	D 5d	2.83	−2.83	76	66.18	66.18	89.24	89.24	87	66.87	66.87	89.24	89.24
^aThe compounds 66–76 and77–87 were not synthesized and reported before.

FIGURE 2 The relationship between the number of carbon atoms “n” and the first free energy of electron transfer (ΔG _et(1), kcal·mol⁻¹) of La@C₈₂@[SWCNT(5,5)-armchair-C_nH₂₀]30–47.

FIGURE 3 The relationship between the number of carbon atoms “n” and the first free energy of electron transfer (ΔG _et(1), kcal·mol⁻¹) of Y@C₈₂@[SWCNT(5,5)-armchair-C_nH₂₀]48–65.

FIGURE 4 The relationship between the number of carbon atoms “n” and the second free energy of electron transfer (ΔG _et(2), kcal·mol⁻¹) of La@C₈₂@[SWCNT(5,5)-armchair-C_nH₂₀]30–47 and Y@C₈₂@[SWCNT(5,5)-armchair-C_nH₂₀]48–65.

Suzuki , T. , Kikuchi , K. , Oguri , F. , Nakao , Y. , Suzuki , S. Achiba , Y. 1996 . Electrochemical properties of fullerenolanthanides . Tetrahedron , 52 : 4973 – 4982 . (and literature cited therein)

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