Electronic Structure and Stability of Binary Metal Cluster with Core-Shell Structure: Theoretical Approach

Abstract

複数の金属元素からなる複合金属クラスターや微粒子は，貴金属減量触媒や卑金属触媒の候補として興味がもたれ，自動車排気ガス浄化触媒，燃料電池電極触媒などの実験分野で活発に研究がおこなわれている．新規な触媒の効率的な設計のためには，電子状態理論計算による複合金属クラスターの電子状態と安定構造, 分子吸着特性, 反応性の相関に対する知見が不可欠である．最近，銅とVIII族からXI族までの金属の複合クラスター(Cu₃₂M₆; M = Ru, Rh, Pd, Ag, Os, Ir, Pt, Au) ，および白金とVIII，IX族金属との複合クラスター(Pt₄₂M₁₃; M = Ru, Rh, Os, Ir)に関して統一的な電子状態理論研究がおこなわれ，シェルからコアへの電荷移動がコアシェル型構造の安定性を決める一つの重要な因子であることが報告された．本総説では，それらのコアシェル型構造の安定性と電子状態，安定性を支配する因子に関する議論をまとめて紹介する．

Figures

Scheme 1.

Schematic representation of (a) Cu₃₇M isomers, (b) investigated isomers of Cu₃₂M₆, and (c) atomic labels of Pt₄₂M₁₃ clusters.

Adapted with permission from J. Phys. Chem. C, 121, 10514 (2017) and J. Phys. Chem. C, 121, 10514 (2017). Copyright (2018) American Chemical Society.

Figure 1.

 Segregation energy (E_seg) as a function of the difference in d orbital population of M between Cu₃₇M (core) and the atomic ground state.

Reprinted with permission from J. Phys. Chem. C, 121, 10514 (2017). Copyright (2018) American Chemical Society.

Scheme 2.

Schematic representation of the most stable structure of Cu₃₂M₆ clusters.

Adapted with permission from J. Phys. Chem. C, 121, 10514 (2017). Copyright (2018) American Chemical Society.

Figure 2.

 (a) Relationship of interaction energy (E_int) between Pt₄₂ shell and M₁₃ core with the reverse of HOMO−LUMO energy gap (Δε_LU‐HO⁻¹) and (b) relationship between E_seg and Δε_LU‐HO⁻¹(Note: Δε_LU‐HO is the energy difference between the LUMO of M₁₃ core and HOMO of Pt₄₂ shell).

Reprinted with permission from J. Phys. Chem. C, 122, 9081 (2018). Copyright (2018) American Chemical Society.

Figure 3.

 HOMO (B3LYP-calculated orbital energy (in eV unit)) and DOSs (these DOSs were calculated by PBE-D2/plane wave basis sets using VASP program) of icosahedral Pt₄₂M₁₃ (M = Ru and Rh) and Pt₅₅ clusters. The Fermi level is shown in the dashed line.

Adapted with permission from J. Phys. Chem. C, 122, 9081 (2018). Copyright (2018) American Chemical Society.

Tables

Table 1.  Relative energy (E_rel in kcal/mol), NBO charge of M (q in e), and d orbital population (q_d) and difference in d orbital population (Δq_d) of M in Cu₃₇M (M = Ru, Rh, Pd, Ag, Os, Ir, Pt, and Au).

		core-shell structure	most stable non-core-shell structure
Cu37Ru
	Erel	0.0	Cu37Ru (face)	+13.6
	q[Ru]	-2.13
	qd (Δqd)	8.55 (+1.55)
Cu37Rh
	Erel	0.0	Cu37Rh (face)	+4.1
	q[Rh]	-1.79
	qd (Δqd)	9.22 (+1.22)
Cu37Pd
	Erel	0.0	Cu37Pd (face)	-6.2
	q[Pd]	-1.28
	qd (Δqd)	9.65 (+0.65)
Cu37Ag
	Erel	0.0	Cu37Pd (corner)	-20.5
	q[Ag]	-0.74
	qd (Δqd)	9.89 (−1.11)
Cu37Os
	Erel	0.0	Cu37Os (face)	+18.7
	q[Os]	-2.15
	qd (Δqd)	8.34 (+1.34)
Cu37Ir
	Erel	0.0	Cu37Ir (face)	+9.5
	q[Ir]	-1.99
	qd (Δqd)	9.04 (+1.04)
Cu37Pt
	Erel	0.0	Cu37Pt (face)	-1.0
	q[Pt]	-1.71
	qd (Δqd)	9.63 (+0.63)
Cu37Au
	Erel	0.0	Cu37Au (corner)	-15.3
	q[Au]	-1.14
	qd (Δqd)	9.87 (−0.13)
Cu38
	Erel	0.0	-	-
	q[Cu]	-0.60
	qd (Δqd)	9.86 (−0.14)

Table 2.  Relative energies (in kcal/mol) of isomers of Cu₃₂M₆.

	a	b	c	d	e
	core-shell			fused-alloy	phase-separated
Cu32Ru6a)	0.0	+16.4	+34.8	+80.0	+101.1
Cu32Rh6b)	0.0	+19.5	+18.3	+47.0	+104.3
Cu32Pd6b)	0.0	-6.1	-7.6	-33.4	+24.9
Cu32Ag6a)	0.0	-16.9	-19.0	-109.6	-108.1
Cu32Os6b)	0.0	+33.0	+76.5	+182.3	+128.9
Cu32Ir6a)	0.0	+29.4	+38.9	+93.6	+139.1
Cu32Pt6b)	0.0	-5.5	-12.4	-51.6	+35.3
Cu32Au6a)	0.0	-23.7	-26.9	-141.2	-97.6

^a) Triplet state.

^b) Singlet state

Table 3.  Relative energy (E_rel in kcal/mol), NBO charge of M (q in e), and d orbital population (q_d) and difference in d orbital population (Δq_d) of M in Pt₄₂M₁₃ (M = Ru, Rh, Os, and Ir).

		core-shell structure	most stable non-core-shell structure
Pt42Ru13
	Erel	0.0	Pt41Ruvertex(Ru12Pt)core	+31.0
	q[Rucore-1]	-3.685
	qd (Δqd)	8.32 (+1.32)
	q[Rucore-2]	-1.433
	qd (Δqd)	8.03 (+1.03)
Pt42Rh13
	Erel	0.0	Pt41Rhvertex(Rh12Pt)core	+6.9
	q[Rhcore-1]	-3.220
	qd (Δqd)	9.13 (+1.13)
	q[Rhcore-2]	-1.774
	qd (Δqd)	9.26 (+1.26)
Pt42Os13
	Erel	0.0	Pt41Osvertex(Os12Pt)core	+61.2
	q[Oscore-1]	-2.274
	qd (Δqd)	8.45 (+2.45)
	q[Oscore-2]	-1.552
	qd (Δqd)	7.80 (+1.80)
Pt42Ir13
	Erel	0.0	Pt41Iredge(Ir12Pt)core	+41.5
	q[Ircore-1]	-1.425
	qd (Δqd)	8.23 (+1.23)
	q[Ircore-2]	-0.893
	qd (Δqd)	8.29 (+1.29)

Reprinted with permission from J. Phys. Chem. C, 122, 9081 (2018). Copyright (2018) American Chemical Society.

Table 4.  Averaged M-M distance (in angstrom) in the M₆ core, averaged Cu-Cu distance in the C₃₂ shell, and deformation energy (E_def in kcal/mol) of the Cu₃₂ shell in Cu₃₂M₆(core).

	M-M	M-Cu	Cu-Cu
	core-core	core-face	core-corner	face-corner	corner-corner		Edefa)
					(i)b)	(ii)c)
Cu38d)	2.572	2.629	2.540	2.550	2.556	2.541	-
Cu32Ru6d)	2.684	2.701	2.562	2.616	2.581	2.646	19.9
Cu32Rh6e)	2.772	2.663	2.528	2.618	2.591	2.644	23.9
Cu32Pd6e)	2.880	2.677	2.537	2.631	2.684	2.578	40.3
Cu32Ag6d)	2.837	2.808	2.590	2.640	2.740	2.526	46.8
Cu32Os6e)	2.657	2.694	2.577	2.624	2.566	2.677	22.9
Cu32Ir6d)	2.738	2.686	2.543	2.617	2.592	2.639	22.3
Cu32Pt6e)	2.946	2.669	2.533	2.644	2.711	2.677	50.9
Cu32Au6d)	2.937	2.791	2.580	2.652	2.784	2.513	61.7

^a) E_def = E(Cu₃₂-shell of Cu₃₂M₆(core)) − E(Cu₃₂-shell of Cu₃₈)

^b) The Cu-Cu distance between corner Cu atoms in the same Cu (100) surface.

^c) The Cu-Cu distance between corner Cu atoms in the different Cu (100) surfaces.

^d) Triplet state.

^e) Singlet state.

Reprinted with permission from J. Phys. Chem. C,121, 10514 (2017). Copyright (2018) American Chemical Society.

参考文献

• [1]   M. Haruta, T. Kobayashi, H. Sano, N. Yamada, Chem. Lett., 16, 405 (1987). doi:10.1246/cl.1987.405
• [2]   H. Kobayashi, K. Kusada, H. Kitagawa, Acc. Chem. Res., 48, 1551 (2015). doi:10.1021/ar500413e25993560
• [3]   K. Kusada, H. Kobayashi, R. Ikeda, Y. Kubota, M. Takata, S. Toh, T. Yamamoto, S. Matsumura, N. Sumi, K. Sato, K. Nagaoka, H. Kitagawa, J. Am. Chem. Soc., 136, 1864 (2014). doi:10.1021/ja409464g24455969
• [4]   H. C. Tsai, Y. C. Hsieh, T. H. Yu, Y. J. Lee, Y. H. Wu, B. V. Merinov, P. W. Wu, S. Y. Chen, R. R. Adzic, W. A. Goddard, III, ACS Catal., 5, 1568 (2015). doi:10.1021/cs501020a
• [5]   B. B. Xiao, Y. F. Zhu, X. Y. Lang, Z. Wen, Q. Jiang, Sci. Rep., 4, 5205 (2015). doi:10.1038/srep0520524902886
• [6]   S. H. Noh, M. H. Seo, J. K. Seo, P. Fischer, B. Han, Nanoscale, 5, 8625 (2013). doi:10.1039/c3nr02611f23897215
• [7]   M. J. Piotrowski, P. Piquini, J. L. F. Da Silva, J. Phys. Chem. C, 116, 18432 (2012). doi:10.1021/jp302844f
• [8]   R. Ferrando, J. Jellinek, R. L. Johnston, Chem. Rev., 108, 845 (2008). doi:10.1021/cr040090g18335972
• [9]   S. Núñez, R. L. Johnston, J. Phys. Chem. C, 114, 13255 (2010). doi:10.1021/jp1048088
• [10]   A. Rapallo, G. Rossi, R. Ferrando, A. Fortunelli, B. C. Curley, L. D. Lloyd, G. M. Tarbuck, R. L. Johnston, J. Chem. Phys., 122, 194308 (2005). doi:10.1063/1.189822316161574
• [11]   D. J. Borbón-González, A. Fortunelli, G. Barcaro, L. Sementa, R. L. Johnston, A. Posada-Amarillas, J. Phys. Chem. A, 117, 14261 (2013). doi:10.1021/jp410079t24303915
• [12]   D. T. Tran, R. L. Johnston, Phys. Chem. Chem. Phys., 11, 10340 (2009). doi:10.1039/b912501a19890518
• [13]   J. P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett., 77, 3865 (1996). doi:10.1103/PhysRevLett.77.386510062328
• [14]   S. Grimme, J. Antony, S. Ehrlich, H. Krieg, J. Chem. Phys., 132, 154104 (2010). doi:10.1063/1.338234420423165
• [15]   A. D. Becke, Physical Review A, 38, 3098 (1988). doi:10.1103/PhysRevA.38.3098
• [16]   A. D. Becke, J. Chem. Phys., 98, 5648 (1993). doi:10.1063/1.464913
• [17]   C. Lee, W. Yang, R. G. Parr, Phys. Rev. B, 37, 785 (1988). doi:10.1103/PhysRevB.37.785
• [18]   G. Kresse, J. Hafner, Phys. Rev. B, 47, 558 (1993). doi:10.1103/PhysRevB.47.558
• [19]   G. Kresse, J. Hafner, Phys. Rev. B, 49, 14251 (1994). doi:10.1103/PhysRevB.49.14251
• [20]   G. Kresse, D. Joubert, Phys. Rev. B, 59, 1758 (1999). doi:10.1103/PhysRevB.59.1758
• [21]   B. Delley, J. Chem. Phys., 92, 508 (1990). doi:10.1063/1.458452
• [22]   B. Delley, J. Chem. Phys., 113, 7756 (2000). doi:10.1063/1.1316015
• [23]   R. Ahlrichs, M. Bär, M. Häser, H. Horn, C. Kölmel, Chem. Phys. Lett., 162, 165 (1989). doi:10.1016/0009-2614(89)85118-8
• [24]   M. J. Frisch, et al., Gaussian 09; Gaussian, Inc., Wallingford CT, 2009.
• [25]   M. W. Schmidt, K. K. Baldridge, J. A. Boatz, S. T. Elbert, M. S. Gordon, J. H. Jensen, S. Koseki, N. Matsunaga, K. A. Nguyen, S. Su, T. L. Windus, M. Dupuis, J. A. Montgomery, J. Comput. Chem., 14, 1347 (1993). doi:10.1002/jcc.540141112
• [26]   K. Ishimura, SMASH-1.1.0. http://smash-qc.sourceforge.net/.
• [27]   T. Nakajima, M. Katouda, M. Kamiya, Y. Nakatsuka, Int. J. Quantum Chem., 115, 349 (2015), Also see http://labs.aics.riken.jp/nakajimat_top/ntchem_e.html. doi:10.1002/qua.24860
• [28]   L. L. Wang, D. D. Johnson, J. Am. Chem. Soc., 131, 14023 (2009). doi:10.1021/ja903247x19754042
• [29]   A. V. Ruban, H. L. Skriver, J. K. Nørskov, Phys. Rev. B, 59, 15990 (1999). doi:10.1103/PhysRevB.59.15990
• [30]   N. Takagi, K. Ishimura, M. Matsui, R. Fukuda, M. Ehara, S. Sakaki, J. Phys. Chem. C, 121, 10514 (2017). doi:10.1021/acs.jpcc.6b13086
• [31]   P. J. Hay, W. R. Wadt, J. Chem. Phys., 82, 299 (1985). doi:10.1063/1.448975
• [32]   J. Lu, K. Ishimura, S. Sakaki, J. Phys. Chem. C, 122, 9081 (2018). doi:10.1021/acs.jpcc.8b01912
• [33]   T. Yamamoto, T. Tanaka, R. Kuma, S. Suzuki, F. Amano, Y. Shimooka, Y. Kohno, T. Funabiki, S. Yoshida, Phys. Chem. Chem. Phys., 4, 2449 (2002). doi:10.1039/b201120b
• [34]   R. Fukuda, N. Takagi, S. Sakaki, M. Ehara, J. Phys. Chem. C, 121, 300 (2017). doi:10.1021/acs.jpcc.6b09280
• [35]   J. X. Wang, H. Inada, L. Wu, Y. Zhu, Y. Choi, P. Liu, W. P. Zhou, R. R. Adzic, J. Am. Chem. Soc., 131, 17298 (2009). doi:10.1021/ja906764519899768
• [36]   T. Ishimoto, M. Koyama, J. Phys. Chem. Lett., 7, 736 (2016). doi:10.1021/acs.jpclett.5b0275326862885